A sphere has a great circle circumference of 40pi feet. What's its volume?

40pi = 2pi r, so r=20

v = 4/3 pi r^3

Thanks!

To find the volume of a sphere, we need to know its radius. However, we are given the circumference of a great circle, not the radius directly.

The circumference of a great circle is equal to the diameter of a sphere, which is twice the length of the radius (C = 2πr). From the information given, we can determine the radius by dividing the given circumference by 2π.

Given: Circumference = 40π feet
C = 2πr

Dividing the given circumference by 2π:
40π / 2π = 20 feet

Hence, the radius of the sphere is 20 feet.

Now, we can use the formula for the volume of a sphere to find the answer. The formula for the volume of a sphere is V = (4/3)πr³.

Substituting the value of the radius into the formula, we get:
V = (4/3)π(20³)

Calculating this expression, we have:
V = (4/3)π(8000)
V = (32000/3)π

The volume of the sphere is (32000/3)π cubic feet.