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.