Geometry

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# Volume of a Sphere

## Sphere Volume Formula

**V = ^{4}⁄_{3}πr^{3}**

Where

*V*is the volume and

*r*is the radius.

### Example Problems

**Problem 1:**

What is the volume of a sphere with a radius of 10?

Solution:

1.) Plugging the radius into the volume formula, we get:

V = ^{4}⁄_{3}πr^{3}

V = ^{4}⁄_{3}π(10^{3}) = ^{4000}⁄_{3}π

2.) **The volume of the sphere is ^{4000}⁄_{3}π.**

**Problem 2:**

What is the volume of a sphere with a diameter of 10?

Solution:

1.) Dividing the diameter by 2 to find radius, we get:

10/2 = 5

r = 5

2.) Plugging the radius into the volume formula, we get:

V = ^{4}⁄_{3}πr^{3}

V = ^{4}⁄_{3}π(5^{3}) = ^{500}⁄_{3}π

3.) **The volume of the sphere is ^{500}⁄_{3}π.**