{"id":27354,"date":"2023-04-11T09:05:06","date_gmt":"2023-04-11T09:05:06","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=27354"},"modified":"2024-02-05T15:28:18","modified_gmt":"2024-02-05T15:28:18","slug":"sector-of-a-circle-definition-formula-area-perimeter-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/sector-of-a-circle","title":{"rendered":"Sector of a Circle: Definition, Formula, Area, Perimeter, Examples"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-73a8756b-2721-461d-a079-244724676416\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/sector-of-a-circle#0-what-is-a-sector-of-a-circle>What Is a Sector of a Circle?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/sector-of-a-circle#4-sector-of-a-circle-formulas>Sector of a Circle Formulas<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/sector-of-a-circle#10-solved-examples-on-sector-of-a-circle>Solved Examples On Sector of a Circle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/sector-of-a-circle#11-practice-problems-on-sector-of-a-circle>Practice Problems On Sector of a Circle<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/sector-of-a-circle#12-frequently-asked-questions-on-sector-of-a-circle>Frequently Asked Questions On Sector of a Circle<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-a-sector-of-a-circle\">What Is a Sector of a Circle?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>A sector of a circle is a portion or part of a circle that is composed of an arc and its two radii. <\/strong>You can compare the sector of a circle to the shape of a pizza slice. A sector is formed when two radii of the circle meet at both ends of the arc. An arc is simply a portion of the circumference of the circle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"312\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/pizza-slices-and-sectors-of-a-circle.png\" alt=\"Pizza slices and sectors of a circle\" class=\"wp-image-37314\" title=\"Pizza slices and sectors of a circle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/pizza-slices-and-sectors-of-a-circle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/pizza-slices-and-sectors-of-a-circle-300x151.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-sector-of-a-circle-definition\">Sector of a Circle Definition<\/h3>\n\n\n\n<p class=\"eplus-wrapper\"><strong>The definition of the sector of a circle in geometry can be given as the part of the circle enclosed by two radii and an arc of the circle. The arc of the circle is a part of the boundary\/circumference of the circle.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"446\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/sector-of-a-circle-angle-arc-and-radii.png\" alt=\"Sector of a circle, angle, arc, and radii\" class=\"wp-image-37315\" title=\"Sector of a circle, angle, arc, and radii\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/sector-of-a-circle-angle-arc-and-radii.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/sector-of-a-circle-angle-arc-and-radii-300x216.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Two radii meet at the center of the circle to form two sectors.&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Minor sector<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Major sector<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"2-minor-sector\">Minor Sector<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">A sector of a circle is called the minor sector if the minor arc of the circle is a part of its boundary. It is the sector with a smaller area. The angle of a minor sector is less than 180 degrees.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"3-major-sector\">Major Sector<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">A sector is called the major sector if the major arc of the circle is a part of its boundary.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">It is the sector with the greater area. The angle of a major sector is greater than 180 degrees.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"369\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/minor-and-major-sectors-of-a-circle.png\" alt=\"Minor and major sectors of a circle\" class=\"wp-image-37316\" title=\"Minor and major sectors of a circle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/minor-and-major-sectors-of-a-circle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/minor-and-major-sectors-of-a-circle-300x179.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/count-upto-10-objects-in-circle\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/count_comp_hide_and_seek_10_gm.png\" alt=\"Count upto 10 Objects in Circle Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Count upto 10 Objects in Circle Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-circles-and-rectangles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_circles_rectangles_pt.png\" alt=\"Identify Circles and Rectangles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Circles and Rectangles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/match-rectangles-and-circles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_amusement_park_3_6_gm.png\" alt=\"Match Rectangles and Circles Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Match Rectangles and Circles Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-sector-of-a-circle-formulas\">Sector of a Circle Formulas<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Let&#8217;s learn how to find the area of a sector of a circle. The formula for determining the area of a sector is given in two ways, with an angle and without an angle.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"5-area-of-a-sector-formula-when-angle-is-given\">Area of a Sector Formula: When Angle Is Given<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">If the radius of a circle is given as \u201cr\u201d and the angle of the sector is given as . This angle is made by the two radii at the center.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"317\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/sector-of-a-circle.png\" alt=\"Sector of a circle\" class=\"wp-image-37317\" title=\"Sector of a circle\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/sector-of-a-circle.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/sector-of-a-circle-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">As we know, for a complete circle, the angle made at the center is equal to 2 or $360^\\circ$.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">If is measured in degrees, then \u201cthe area of a sector of a circle formula\u201d is given by<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Area of sector <\/strong>$= \\frac{\\theta}{360^\\circ} \\times \\pi r^2$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">If is measured in radians, then \u201cthe area of a sector of a circle formula\u201d is given by<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Area of sector <\/strong>$= \\frac{1}{2} \\times \\theta \\times r^2$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Perimeter of sector $=2r + \\frac{\\theta}{360} \\times 2\\pi r$<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"6-area-of-sector-formula-when-angle-is-not-given\">Area of Sector Formula: When Angle Is Not Given<\/h3>\n\n\n\n<p class=\"eplus-wrapper\">How can we find the area of a sector of a circle when the central angle is not given? Let\u2019s find out.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If l is the length of the arc, r is the radius of the circle and \u03b8 is the angle subtended at the center, then the angle is expressed in terms of l and r as<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\theta = \\frac{l}{r}$, where is in radians.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If the angle of the sector $=2\\pi$, the area of the sector (full circle) is $r^2$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Similarly, for the angle $= 1$, the area of the sector $= \\frac{\\pi r^2}{2\\pi} = \\frac{r^2}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, for the angle , area of the sector $\\theta = \\frac{r^2}{2} = \\frac{l}{r}\\times\\frac{r^2}{2} = \\frac{lr}{2}$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Area of the sector without an angle $= \\frac{lr}{2}$.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Perimeter of sector $= 2r + l$<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"7-arc-length-of-a-sector-formula\">Arc Length of a Sector Formula<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"335\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/arc-length-of-a-sector.png\" alt=\"Arc length of a sector\" class=\"wp-image-37318\" title=\"Arc length of a sector\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/arc-length-of-a-sector.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/arc-length-of-a-sector-300x162.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">The length of the arc \u201cl\u201d of the sector with angle is given by:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$l = \\frac{\\theta}{360}\\times2\\pi r$&nbsp; \u2026when $\\theta$ is given in degrees<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$l = \\theta r$ \u2026when$\\theta$ is given in radians<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/circle-equivalent-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/circle-equivalent-fractions.jpeg\" alt=\"Circle Equivalent Fractions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/squares-and-circles\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/squares-and-circles.jpeg\" alt=\"Squares and Circles Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-facts-about-sector-of-a-circle\">Facts about Sector of a Circle<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">A section or part of a circle involved by two radii with a central angle $90^\\circ$ is called a quadrant.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">A section or part of a circle involved by two radii with a central angle of $180^\\circ$ is called a semicircle.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The combination of any two hands (minute hands and hour hands or hour hands and second hands or minute hands and second hands) of a circular analog clock form sectors.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this article, we learned about the sector of a circle, minor and major sector, the sector formula for area, perimeter and arc length with and without angle. Now, let us look at some solved examples and practice questions.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-solved-examples-on-sector-of-a-circle\">Solved Examples On Sector of a Circle<\/h2>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Calculate the area of the sector.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"192\" height=\"151\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/area-of-sector-of-a-circle.png\" alt=\"Area of sector of a circle\" class=\"wp-image-37319\" title=\"Area of sector of a circle\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The radius of sector $= r = 6$ inches<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Angle of sector $= \\theta = 60^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The area of sector $= \\frac{\\theta}{360^\\circ}\\times\\pi r^2 = \\frac{60^\\circ}{360^\\circ}\\times3.14\\times6^2 = 18.84$ sq. in.<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Find the area of a sector of a circular region whose central angle is 3 radians with a radius of 5 feet.<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The radius of sector $= r = 5$ feet<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Angle of sector $= \\theta = 3$ radians<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If is measured in radians, then<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The area of the sector $= \\frac{\\theta}{2}\\times r^2 = \\frac{3}{2}\\times5^2 =37.5$ sq. feet.<\/p>\n\n\n\n<ol start=\"3\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Find the central angle of a sector (in degrees) which has a 25 sq. yard area and a radius of 4 yards. Use $<\/strong>\\pi = 3.14$<strong>.<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Radius of sector $= r = 4$ yards<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of sector $= 25$ sq. yards<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If is measured in degrees, then<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of the sector $= \\frac{\\theta}{360^\\circ} \\times \\pi r^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$25 = \\frac{\\theta}{360^\\circ}\\times3.14\\times4^2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\theta = \\frac{25\\times360}{3.14\\times4^2} = 179.14^0$<\/p>\n\n\n\n<ol start=\"4\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Find the perimeter of the sector shown below.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"203\" height=\"212\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/perimeter-of-sector-of-a-circle.png\" alt=\"Perimeter of sector of a circle\" class=\"wp-image-37320\" title=\"Perimeter of sector of a circle\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The radius of sector $= r = 8$ inches<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Angle of sector $= \\theta = 115^\\circ$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The perimeter of sector $= 2r + \\frac{\\theta}{360}\\times2\\pi r$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$=(2\\times8) + \\frac{115^\\circ}{360^\\circ}\\times(2\\times3.14\\times8)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$=16 + (\\frac{1}{4}\\times23.14\\times8)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$=16 + 12.56$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$=28.56$ in<\/p>\n\n\n\n<ol start=\"5\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Find the area and perimeter of a sector with a radius of 10 feet and an arc length of 12.56 feet.<\/strong><\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The radius of sector $= r = 10$ feet<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Arc length $= l = 12.56$ feet<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Area of the sector without an angle $= \\frac{lr}{2} = \\frac{12.56\\times10}{2}=62.8$ sq. feet<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Perimeter of sector $= 2r + l = 2(10) + 12.56 = 32.56$ feet.<\/p>\n\n\n\n<ol start=\"6\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Find the arc length of a sector having a radius of 5 feet and a central angle of <\/strong>$120^\\circ$<strong>.<\/strong><\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"147\" height=\"139\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/sector-of-a-circle-1.png\" alt=\"Sector of a circle\" class=\"wp-image-37321\" title=\"Sector of a circle\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The radius of sector $= r = 5$ feet<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Angle of sector $= \\theta = 120^\\circ$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The length of the arc \u201cl\u201d of the sector with angle is given by;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$l = \\frac{\\theta \\pi r}{180} = \\frac{120\\times3.14\\times5}{180} = 10.47$ feet<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-practice-problems-on-sector-of-a-circle\">Practice Problems On Sector of a Circle<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Sector of a Circle: Definition, Formula, Area, Perimeter, Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">The sector of a circle is formed by two ____ and an arc.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">chords<\/div><div class=\"spq_answer_block\" data-value=\"1\">diameters<\/div><div class=\"spq_answer_block\" data-value=\"2\">radii<\/div><div class=\"spq_answer_block\" data-value=\"3\">tangents<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: radii<br\/>The sector of a circle is formed by two radii and an arc.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The central angle of the minor sector is _________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">less than 270 degrees<\/div><div class=\"spq_answer_block\" data-value=\"1\">less than 180 degrees<\/div><div class=\"spq_answer_block\" data-value=\"2\">more than 270 degrees<\/div><div class=\"spq_answer_block\" data-value=\"3\">more than 180 degrees<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: less than 180 degrees<br\/>The central angle of the minor sector is less than 180 degrees.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">For the quadrant of a circle, the central angle is _________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$90^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$180^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$60^\\circ$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$45^\\circ$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $90^\\circ$<br\/>The quadrant of a circle can be a sector of a circle with a central angle of $90^\\circ$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">If$\\theta$is measured in radians, then the formula for the area of a sector of a circle is equal to ____________.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Area of sector $=\\frac{\\theta}{180^\\circ}\\times\\pi r^2$<\/div><div class=\"spq_answer_block\" data-value=\"1\">Area of sector $=\\frac{\\theta}{360^\\circ}\\times\\pi r^2$<\/div><div class=\"spq_answer_block\" data-value=\"2\">Area of sector $=\\theta r^2$<\/div><div class=\"spq_answer_block\" data-value=\"3\">Area of sector $=\\frac{\\theta}{2}\\times r^2$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Area of sector $=\\frac{\\theta}{2}\\times r^2$<br\/>If $\\theta$ is measured in radians, then<br>\r\nArea of sector $= \\frac{\\theta}{2}\\times r^2$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">The area of the quadrant of a circle is equal to _____ of that of the circle.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{1}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{1}{3}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{1}{4}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{1}{8}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\frac{1}{4}$<br\/>The area of the quadrant of a circle is equal to one-fourth, i.e., $\\frac{1}{4}$ of that of the circle.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": 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\"Comment\",\n                      \"text\": \"The central angle of the minor sector is less than 180 degrees.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"less than 270 degrees\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The central angle of the minor sector is less than 180 degrees.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"more than 270 degrees\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The central angle of the minor sector is less than 180 degrees.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"more than 180 degrees\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The central angle of the minor sector is less than 180 degrees.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"less than 180 degrees\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The central angle of the minor sector is less than 180 degrees.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The central angle of the minor sector is less than 180 degrees.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"For the quadrant of a circle, the central angle is _________.\",\n                    \"text\": \"For the quadrant of a circle, the central angle is _________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The quadrant of a circle can be a sector of a circle with a central angle of $$90^\\\\circ$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$180^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The quadrant of a circle can be a sector of a circle with a central angle of $$90^\\\\circ$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$60^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The quadrant of a circle can be a sector of a circle with a central angle of $$90^\\\\circ$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$45^\\\\circ$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The quadrant of a circle can be a sector of a circle with a central angle of $$90^\\\\circ$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$90^\\\\circ$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The quadrant of a circle can be a sector of a circle with a central angle of $$90^\\\\circ$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The quadrant of a circle can be a sector of a circle with a central angle of $$90^\\\\circ$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If$$\\\\theta$$is measured in radians, then the formula for the area of a sector of a circle is equal to ____________.\",\n                    \"text\": \"If$$\\\\theta$$is measured in radians, then the formula for the area of a sector of a circle is equal to ____________.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"If $$\\\\theta$$ is measured in radians, then<br>\r\nArea of sector $$= \\\\frac{\\\\theta}{2}\\\\times r^2$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Area of sector $$=\\\\frac{\\\\theta}{180^\\\\circ}\\\\times\\\\pi r^2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If $$\\\\theta$$ is measured in radians, then<br>\r\nArea of sector $$= \\\\frac{\\\\theta}{2}\\\\times r^2$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Area of sector $$=\\\\frac{\\\\theta}{360^\\\\circ}\\\\times\\\\pi r^2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If $$\\\\theta$$ is measured in radians, then<br>\r\nArea of sector $$= \\\\frac{\\\\theta}{2}\\\\times r^2$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Area of sector $$=\\\\theta r^2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If $$\\\\theta$$ is measured in radians, then<br>\r\nArea of sector $$= \\\\frac{\\\\theta}{2}\\\\times r^2$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Area of sector $$=\\\\frac{\\\\theta}{2}\\\\times r^2$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"If $$\\\\theta$$ is measured in radians, then<br>\r\nArea of sector $$= \\\\frac{\\\\theta}{2}\\\\times r^2$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"If $$\\\\theta$$ is measured in radians, then<br>\r\nArea of sector $$= \\\\frac{\\\\theta}{2}\\\\times r^2$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The area of the quadrant of a circle is equal to _____ of that of the circle.\",\n                    \"text\": \"The area of the quadrant of a circle is equal to _____ of that of the circle.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The area of the quadrant of a circle is equal to one-fourth, i.e., $$\\\\frac{1}{4}$$ of that of the circle.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The area of the quadrant of a circle is equal to one-fourth, i.e., $$\\\\frac{1}{4}$$ of that of the circle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{3}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The area of the quadrant of a circle is equal to one-fourth, i.e., $$\\\\frac{1}{4}$$ of that of the circle.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{8}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The area of the quadrant of a circle is equal to one-fourth, i.e., $$\\\\frac{1}{4}$$ of that of the circle.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{1}{4}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The area of the quadrant of a circle is equal to one-fourth, i.e., $$\\\\frac{1}{4}$$ of that of the circle.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The area of the quadrant of a circle is equal to one-fourth, i.e., $$\\\\frac{1}{4}$$ of that of the circle.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-frequently-asked-questions-on-sector-of-a-circle\">Frequently Asked Questions On Sector of a Circle<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-cc431d36-6261-4aa3-8184-718c07221a0b\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-cc431d36-6261-4aa3-8184-718c07221a0b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cc431d36-6261-4aa3-8184-718c07221a0b\"><strong>What is the difference between a sector and an arc?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-cc431d36-6261-4aa3-8184-718c07221a0b\">\n\n<p class=\"eplus-wrapper\">Arc represents the part of the circumference. The sector of a circle is a part of the circle that is enclosed by two radii and an arc of the circle as a part of its boundary.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-cc431d36-6261-4aa3-8184-718c07221a0b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cc431d36-6261-4aa3-8184-718c07221a0b\"><strong>What is the area of the sector of a circle composed of?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-cc431d36-6261-4aa3-8184-718c07221a0b\">\n\n<p class=\"eplus-wrapper\">The area of the sector of a circle is the area of the part of a circle composed of an arc and two radii.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-cc431d36-6261-4aa3-8184-718c07221a0b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cc431d36-6261-4aa3-8184-718c07221a0b\"><strong>What is the formula for the perimeter of a sector of a circle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-cc431d36-6261-4aa3-8184-718c07221a0b\">\n\n<p class=\"eplus-wrapper\">The perimeter of a sector is formed by two radii and an arc.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Perimeter of the sector $= 2r + l = 2r + \\frac{\\theta}{360} \\times 2\\pi r$,&nbsp;where $r =$ radius of the circle, $l =$ arc length, $\\theta =$ angle of the sector.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-cc431d36-6261-4aa3-8184-718c07221a0b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cc431d36-6261-4aa3-8184-718c07221a0b\"><strong>How many types of sectors are in a circle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-cc431d36-6261-4aa3-8184-718c07221a0b\">\n\n<p class=\"eplus-wrapper\">There are two types of a sector, which can be categorized as a minor or a major part.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-cc431d36-6261-4aa3-8184-718c07221a0b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cc431d36-6261-4aa3-8184-718c07221a0b\"><strong>What is the formula for the area of a sector without an angle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-cc431d36-6261-4aa3-8184-718c07221a0b\">\n\n<p class=\"eplus-wrapper\">Area of the sector without an angle $= \\frac{lr}{2}$, where $r =$ radius of the circle, $l =$ arc length.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-5-cc431d36-6261-4aa3-8184-718c07221a0b\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cc431d36-6261-4aa3-8184-718c07221a0b\"><strong>How to find the arc length of a sector of a circle?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-5-cc431d36-6261-4aa3-8184-718c07221a0b\">\n\n<p class=\"eplus-wrapper\">The arc length of a sector of a circle can be found using the formula:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$l = \\frac{\\theta}{360} \\times 2\\pi r$ or,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$l = \\frac{\\theta \\pi r}{180}$. Where, $r =$ radius of the circle, $l =$ arc length, $\\theta =$ angle of the sector.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is a Sector of a Circle? A sector of a circle is a portion or part of a circle that is composed of an arc and its two radii. You can compare the sector of a circle to the shape of a pizza slice. A sector is formed when two radii of the circle &#8230; <a title=\"Sector of a Circle: Definition, Formula, Area, Perimeter, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/sector-of-a-circle\" aria-label=\"More on Sector of a Circle: Definition, Formula, Area, Perimeter, Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-27354","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27354","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=27354"}],"version-history":[{"count":10,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27354\/revisions"}],"predecessor-version":[{"id":39921,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/27354\/revisions\/39921"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=27354"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=27354"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=27354"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}