Math  Help

Volume of a Sphere

What is the volume of a sphere?

The volume of a sphere is the amount of space that a sphere takes up. Imagine a basketball that occupies space. How much space does it occupy?

The volume is to calculate this space. Then how would you calculate volume?

Volume is different from area in that it is 3 dimensional, therefore it will be cubic (cm3, m3, etc.) rather than square.

Equation for Volume of a sphere

The equation for the volume of a sphere is

Note that the only variable is r, which is the radius. Beware that if you are given the diameter, you need to convert into r using this equation:

Your teacher can also ask you to calculate the volume of a hemisphere. What is a hemisphere? Imagine cutting the basketball in half. A hemisphere is half of a sphere, therefore its volume is halved:

Example of Volume of a sphere

Find the volume of the sphere. Round to the nearest cubic centimeter.

 

1) Write the volume of the sphere formula:

2) Find the radius of the sphere from the figure:

3) Substitute 5 cm for r in the formula:

4) Simplify:

Therefore, the volume of the sphere is about 523 cm3.

Practice Problems
for Volume of a sphere

1. Find the volume of the sphere if the diameter is 42 cm. Round to the nearest cubic meter.

 

2. Find the volume of the sphere if it has a radius of 3 cm. Round to the nearest cubic kilometer.

Take Home Points
for Volume of a sphere

• Equation for the volume of a sphere is

• Ensure that the units are correct

• Units are cubic (cm3, m3, etc)

• Convert diameter into radius so you can plug r into the equation

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