# How to Find the Volume of a Sphere

The volume of a sphere is the amount of three dimensional space inside of a sphere. Volume is a three dimensional measurement so it is measured in cubic units like $$in^3$$, $$cm^3$$, and $$ft^3$$.

In real life, you could use it to calculate the amount of ice cream in a perfectly round ball of ice cream. Or the amount of water you would need to fill up a perfectly round water balloon.

Volume is the space inside of a sphere. If you are looking for the amount of flat space on the outside surface of a sphere, that is called the surface area of a sphere and it has a different formula than volume does.

## Volume of a Sphere Formula

$V=\frac{4}{3}\pi r^3$

## How to Find the Volume of a Sphere

1. Find the radius of the sphere.
2. Substitute the radius into the Volume of a Sphere Formula

## Examples

These examples show how to find the volume when you are given the radius or diameter of a sphere. The examples on this page show how to use the Volume of a Sphere Formula to find the radius or diameter of a sphere if you are given the volume.

What is the volume?

What is the radius of the sphere?

The diagram tells me that the radius of the sphere is $$\green 6\, cm$$.

What is the volume?

When I substitute $$\green 6$$ into the volume formula, I get…

$V=\frac{4}{3}\pi ({\green 6})^3$

I can simplify the exponent by multiplying $$\green 6$$ by itself $$3$$ times.

${\green 6}\times {\green 6}\times {\green 6}={\green 216}$

So, that means…

$V=\frac{4}{3}\pi ({\green 216})$

Next, I’ll write $$\green 216$$ as a fraction and multiply the fractions.

$\frac{4}{3}\times\frac{\green 216}{1}={\frac{\green864}{3}}$

$$\green 864$$ is divisible by $$3$$, so I can reduce the fraction.

${\frac{\green 864}{3}}={\green 288}$

So, the simplified volume formula is…

$V={\green 288}\pi$

The volume is $$\green 288\pi \, cm^3$$.

I could find the decimal approximation of the volume by multiplying $$\green 288$$ by $$3.14$$.

$\green V\approx 904.32\, cm^3$

What is the volume?

What is the radius of the sphere?

The diagram shows me that the radius is $$\blue \frac{3}{4}\, in$$.

What is the volume?

When I substitute $$\blue \frac{3}{4}$$ into the volume formula, I get…

$V=\frac{4}{3} \pi \left( {\blue \frac {3}{4}} \right )^3$

I can simplify the exponent by multiplying $$\blue \frac {3}{4}$$ by itself $$3$$ times.
${\blue \frac {3}{4}}\times {\blue \frac {3}{4}}\times {\blue \frac {3}{4}}={\blue \frac {27}{64}}$

So, that means…
$V=\frac{4}{3} \pi \left ({\blue \frac {27}{64}} \right )$

Next, I’ll multiply the fractions.

$\frac{4}{3}\times{\blue \frac {27}{64}}={\blue \frac {108}{192}}$

$$\blue 108$$ and $$\blue 192$$ are both divisible by $$12$$, so I can reduce the fraction.

${\blue\frac{108}{192}}={\blue \frac {9}{16}}$

So, the simplified volume formula is…

$V={\blue \frac{9}{16}}\pi$

The volume is $$\blue \frac{9\pi}{16} \, in^3$$.

I could find the decimal approximation of the volume by multiplying $$\blue \frac{9}{16}$$ by $$3.14$$.

$\blue V\approx 1.76625\, in^3$

What is the volume?

What is the radius of the sphere?

The diagram shows me that the diameter of the sphere is $$\red 2.6\, m$$.

The radius of the sphere is half of the diameter so I can divide $$\red 2.6\, m$$ by $$2$$ to find the radius.

${\red 2.6} \div 2 = {\red 1.3}$

The radius of the sphere is $$\red 1.3 \, m$$.

What is the volume?

When I substitute $$\red 1.3$$ into the volume formula, I get…

$V=\frac{4}{3}\pi \left( {\red 1.3} \right )^3$

I can simplify the exponent by multiplying $$\red 1.3$$ by itself $$3$$ times.
${\red 1.3}\times {\red 1.3}\times {\red 1.3}={\red 2.197}$

So, that means…
$V=\frac{4}{3}\pi \left ({\red 2.197} \right )$

Next, I’ll convert the decimal to a fraction and multiply the fractions

$\frac{4}{3}\times{\red \frac {2197}{1000}}={\red \frac {8788}{3000}}$

$$\red 8788$$ and $$\red 3000$$ are both divisible by $$4$$, so I can reduce the fraction.

${\red\frac{8788}{3000}}={\red \frac {2197}{750}}$

So, the simplified volume formula is…

$V={\red \frac{2197}{750}}\pi$

The volume is $$\red \frac{2197\pi}{750} \, m^3$$.

Or I could find a decimal approximation of the volume by multiplying $$\red \frac{2197}{750}$$ by $$3.14$$.

$\red V\approx 9.1981\, m^3$

## Worksheets & Online Practice

Find the Volume when Given the Whole Number Radius of a Sphere

Find the Volume when Given the Decimal Radius of a Sphere

Find the Volume when Given the Diameter of a Sphere

Find the Volume when Given the Radius and Diameter of a Sphere