Calculate the Volume of a Sphere from Its Circumference

The formula for the volume of a sphere is traditionally given as a function of the radius. However, in practical applications, it is not always easy to determine the diameter or radius of a round object.

The circumference of a ball of sphere is much easier to measure. Simply wrap a measuring tape around the widest part of the sphere (the equator) and record the distance all the way around. And since the circumference and radius are related by a simple formula, you can then determine the radius of the object, and finally the volume.

First recall the formulas for volume (v) and circumference (c) in terms of the radius (r).

v = (4/3)πr³

c = 2πr

If you solve the second equation for r, you get

c/(2π) = r

Now plug this into the volume equation. That is, you replace r with the expression c/(2π).

v = (4/3)π[c/(2π)]³

= (4/3)π[c³/(8π³)]

= c³/(6π²)

An inflatable ball has a circumference of 60 cm. What is the volume of the ball in cubic centimeters (cc)?

Solution: Since c = 60, we plug that value into the equation v = c³/(6π²) to find the volume

v = 60³/(6π²)

= 216000/59.2176

= 3647.5626 cc

= 3.648 liters