SOLUTION: what is the volume (in cm3) of a softball that has a circumference of 27 cm

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Question 219054: what is the volume (in cm3) of a softball that has a circumference of 27 cm
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
A softball is a sphere. The formula for volume of a sphere is:
V+=+%284%2F3%29pi%2Ar%5E3
From this formula we can see that in order to find the volume of a sphere all we need to know is "r" (which is the radius).

But we don't know the radius. We do know the circumference however. The formula for circumference is:
C+=+2pi%2Ar
So with the circumference, we can find the radius:
27+=+2pi%2Ar
Divide both sides by 2pi:
27%2F%282pi%29+=+r
We can now use this in the volume formula:
V+=+%284%2F3%29pi%2A%2827%2F%282pi%29%29%5E3
To find the exact volume, leave pi in the expression and simplify the expression as much as possible:
V+=+%284%2F3%29pi%2A%2819683%2F%288pi%5E3%29%29
One pi cancels and so does a 4 and a 3 leaving:
V+=+%286561%2F%282pi%5E2%29%29 cm%5E3
which is the exact volume. If you want a decimal approximation of the volume, substitute a decimal approximation of pi. (3.14 is commonly used as a decimal approximation for pi.) A decimal approximation of the V is about 332.4 cm%5E3.