You see it in boxes as you grab a tissue or pop open your box of cereal. You see it in books as you remove your bookmarks to begin reading. You see it in laptops as you finish typing your latest assignment.
Yes, we are talking about the rectangular prism.
What Is a Rectangular Prism?
A rectangular prism is a three-dimensional shape with six faces. All the faces (top, bottom, and lateral faces) of the prism are rectangular so that all the pairs of opposite faces are congruent. It is also known as a cuboid. In short, a rectangular prism has four rectangular faces and two parallel rectangular bases.
How is a rectangular prism different from a rectangle?
To begin with, why is it important to know the difference between different types of shapes?
Every shape has distinct properties and these properties help to know quantities such as volume, surface area, etc. Remember, you would not know to not put a rectangle on top of a triangle if you don’t know how they are different.
Difference Between Rectangle & Rectangular Prism
|It is a 2D shape.||It is a 3D shape.|
|It has four sides.||It has six faces, eight verticals & twelve edges.|
|It is made of four sides with the opposite sides having equal lengths.||It is made up of six rectangles put together.|
|It has width and length.||It has width, height and length.|
|It is made of two pairs of lines.||It is made of three pairs of rectangles.|
Now that we know what rectangular prisms are, let’s look at how we can calculate its volume.
The Formula for Volume of a Rectangular Prism
By multiplying the base area of a prism by its height, you will get the volume of a prism. That is to say, the volume of a prism = base area × height.
Since a rectangular prism’s base is a rectangle itself, the volume of a rectangular prism, by applying the formula given above, will be:
Volume of a rectangular prism (V) = l × w × h
“l” means the base length, and
“w” means the base width,
“h” means the height
Example 1: Find out the volume of a rectangular prism with base length 9 inches, base width 6 inches, and height 18 inches, respectively.
Length (l) = 9 inches
Width (b) = 6 inches
Height (h) = 18 inches
So, the volume of the given rectangular prism = l × w × h = 9 × 6 × 18 = 972 cubic inches.
Example 2: Find out the height of a rectangular prism whose base area is 20 sq. units and a volume is 60 cubic units.
Given is the base area of the rectangular prism = 20 sq. units
And the volume of the rectangular prism = 60 cubic units
Now, applying the volume of the rectangular prism formula,
base area × height = 60 cubic units.
⇒ 20 × height = 60
⇒ height = 60 ÷ 20 units
⇒ height = 3 units
Example 3: Find out the base area of a rectangular prism with the help of the given measurements: length = 12 inches, height = 20 inches, and volume = 2,160 cubic inches.
Length (l) = 12 inches
Height (h) = 20 inches
Volume (V) = 2,160 cubic inches
The volume of the rectangular prism = l × w × h
⇒ 2,160 = 12 × w × 20
⇒ 2,160 ÷ (12 × 20) = w
⇒ 9 = w
Therefore, width (w) = 9 inches.
Area = l × w = 12 × 9 = 108 sq. inches.
Volume of Rectangular Prism
Choose the correct formula to determine the volume of a rectangular prism?
V = Base area – height
V = Base area + height
V = Base area × height
V = Base area / height
Correct answer is: V = Base area × height
This essentially means the area of a rectangular prism is length × breadth × height as the base of the rectangular prism is a rectangle.
Find out the base area of a rectangular prism whose height is 7 inches and volume is 343 cubic inches.
7 sq. inches
2,401 sq. inches
49 sq. inches
21 sq. inches
Correct answer is: 49 sq. inches
Base area of rectangular prism = Volume ÷ Height = 343 ÷ 7 = 49 sq. inches
Find out the volume of a rectangular prism whose base area is 35 cm and height is 10 cm.
345 cubic cm
350 cubic cm
354 cubic cm
360 cubic cm
Correct answer is: 350 cubic cm
Volume of rectangular prism = base area × height = (35 × 10) = 350 cubic cm
The volume of a rectangular prism is an important concept for 5th graders to learn. As we have already discussed, the volume of a rectangular prism is the product of its dimensions, i.e., length, width, and height. This can be better understood with practical examples. Using SplashLearn, students can practice each example with online interactive worksheets. This game-based learning app makes learning fun and keeps your child engaged.
Every game on SplashLearn is curriculum-based and scientifically designed. To boost your kid’s knowledge in mathematics and allow them to practice mathematics fearlessly, you can sign up to SplashLearn for free!
Frequently Asked Questions
What is another name for a rectangular prism?
A rectangular prism is also known as a cuboid.
Is the volume of a rectangular prism the same as a cuboid?
Yes, the volume of a rectangular prism is the same as the volume of a cuboid.
What is an oblique rectangular prism?
An oblique rectangular prism is a prism with six rectangular faces, but the lateral faces are not perpendicular to the bases.
What is the surface area of a rectangular prism?
The surface area of a rectangular prism is the sum of the area of each of its faces. It is given by the formula, 2(lw + wh + hl), where l is length, w is width, and h is the height of the rectangular prism.