Volume of a sphere This page explains how to find the volume of a sphere. There are some exercises and solutions on this page too. The formula for the volume of a sphere with radius r: The volume of a sphere formula with diameter d: Volume is expressed in m3 or liters (SI units) or cubic feet and gallons. One cubic meter contains 1000 liters, and it equals 35,3 cubic feet. One cubic foot is equal to 7,48 US gallons. The formulas are the same.
Exercises
1. A sphere has a 4 centimeter radius. Calculate the volume.
2. What is the volume of a sphere with a 10 centimeter diameter?
3. A large balloon has a 400 m3 volume. Calculate the radius.
4. The area of a sphere is 17 m2. Can you calulate the volume?
5. How many cubic feet and gallons is that?
6. The gas in a balloon creates lift. Will two 3 meter diameter balloons create more or less lift than one 5 meter diameter balloon? (The pressure is the same in both balloons.)
Solutions
1. 4/3 * π * 42 = 67 cm3
2. 1/6 * π * 103 = 524 cm3
3. The radius equals 4,75 meter.
4. On the basis of the area of a sphere one can calculate the radius or the diameter. The radius is 1,16, so the volume is 6,6 m3.
5. 6,6 m3 is the same as 6600 liters, 1744 gallons or 233 cubic feet.
6. The two balloons small balloons together have a volume of 28,3 m3. The large balloon has a 65,4 m3 volume, so this one creates more lift. Note that the volume of a sphere changes with the power three of the radius or diameter.

You might want to have a look at our other pages about math, geometry, volumes and shapes!