## Sphere – An Introduction

The sphere is a three-dimensional shape, also called the second cousin of a circle. A sphere is round, has no edges, and is a solid shape. The playing ball, balloon, and even light bulbs are examples of sphere shape.

**How Is the Sphere Different From Other Three-Dimensional Objects?**

Unlike other three-dimensional objects, such as the cube, cone, and cylinder, the **sphere shape** does not have any flat surface, vertex, or edge. It only has a rolling surface.

**Important Elements of a Sphere Shape**

The important elements of a **sphere** are the following:

**Radius:**The distance between the center of a**sphere**and its surface is called the radius. It is denoted by the letter*r*.

**Diameter: **Think of the diameter as the longest straight line you can put inside a sphere. The diameter passes through the center and joins two opposite points on the surface of a sphere. Its value is always twice that of the radius. It is denoted by the letter *d*.* *The formula to calculate the diameter of a **sphere** is 2*r*.* *

*d *$=$* 2r*

**Circumference: **The circumference of a sphere can be defined as the greatest cross-section of a circle that we can cut from a sphere. The formula for the circumference of a sphere is given by 2 $\times$ π $\times$* r.*

*C*$=$* *2 π* r, *where r is the radius of the circle and π (pi) is approximately 3.14.

*Did you know that the equator is one of Earth’s great circles? If you were to cut into the Earth right on its equator, you’d have two halves: the northern and southern hemispheres.*

**Surface Area: **The surface area of a sphere is the total area of its rolling surface. The formula to calculate the surface area of a sphere is given by,

*SA *$=$* 4 r2 ***, **where r is the radius of the circle and π(pi) is approximately 3.14.

It is measured in square units.

**Volume: **The volume of a sphere can be defined as the capacity of a liquid that the sphere would hold if it were completely hollow. For example, the amount of water you can fill in an earthen pot defines its volume as a spherical object. The formula to calculate the volume of a sphere is given by,

*V *$= \frac{4}{3} r^3$. It is measured in cubic units.

**Solved Examples**

**Example 1: If the radius of a sphere is 5 cm, find its circumference.**

**Solution:**

We know that the circumference of a sphere is given by

C $= 2 \times$ π $\times$* r.*

For the given sphere, r $= 5$ cm.

Therefore, circumference of the given sphere $= 2 \times 3.14 \times 5 = 31.4$ cm.

**Example 2: If the radius of a sphere is 10 cm, find its surface area.**

**Solution:**

We know that the surface area of a sphere is given by

Surface Area $= 4$* r2*

For the given sphere, r $= 10$ cm.

Substituting the value of “*r*” in the formula, we get,

SA $= 4 \times 3.14 \times 10 \times 10$

SA $= 4 \times 3.14 \times 100$

SA $= 1256$ cm²

Therefore, the surface area** **of this** **sphere is** **$1256$ cm².

**Example 3: What is the volume of a sphere of radius 7 cm?**

**Solution:**

We know that the volume of a sphere is given by

*V *$= 43$* r3*

For the given sphere, r $= 7$ cm

V $= 43 \times 3.14 \times 7 \times 7 \times 7$

V $= 43 \times 3.14 \times 343$

V $= 1436.02$** **cm³ Therefore, the volume** **of the given sphere is $1436.02$ cm³

## Practice Problems

## Sphere - Definition With Examples

### 1If the radius of a sphere is 25 cm, find its diameter.

We know that the diameter of a sphere is given by d $=$ 2r, where r is the radius.

For the given sphere, r $= 25$ cm

Therefore, diameter of the given sphere $= 2 \times 25 = 50$ cm

### 2If the diameter of a sphere is 64 cm, find its radius.

We know that the diameter of the sphere is given by d $= 2$r.

Where the radius is r.

Therefore, for the given sphere:

$64 = 2 \times$r

Therefore, r $= \frac{64}{2} = 32$ cm.

And we get 32 cm as our answer.

### 3If the radius of a sphere is 14 cm, find its circumference.

The formula for calculating the circumference of a sphere $= 2$$π$r

The radius of the given sphere $= 14$ cm

Therefore, Circumference of the given sphere $= 2 \times 3.14 \times 14 = 87.92$ cm

### 4If the radius of a sphere is 20 cm, find its surface area.

The radius of the given sphere $= 21$ cm

The formula for calculating the surface area of a sphere, $4πr²$

Therefore,

The surface area of a given sphere $= 4 \times 3.14 \times 20 \times 20 = 4 \times 3.14 \times 400 = 5024$ cm$^{2}$

## Frequently Asked Questions

**What is a hemisphere?**

Simply put, the hemisphere is half of a **sphere**. If you cut a **sphere** into exactly two halves, each half would be considered a hemisphere.

**What are the differences between a circle and a sphere?**

To begin with, a circle and a **sphere** are different shapes. The following are a few of the main differences between them:

**Circle: **A circle is a two-dimensional shape. It refers to a closed curved line. A circle does not have any volume.

**Sphere: **A sphere has a three-dimensional shape. It is a round object. A sphere has volume.

**Give a few common examples of spheres in real life.**

Marbles, balls, oranges, yarn, and bubbles are a few common examples of sphere shapes in real life.