Question 255274: The surface area of a sphere is 3600 pi square inches. If v represents the volume of the sphere in cubic inches, what is v/pi ?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! formula for the surface area of a sphere is:
s = 4 * pi * r^2
formula for the volume of a sphere is:
v = (4/3) * pi * r^3
since s = 4 * pi * r^2, and since s = 3600 * pi, then we get:
3600 * pi = 4 * pi * r^2
divide both sides of this equation by pi to get:
3600 = 4 * r^2
divide both sides of this equation by 4 to get:
900 = r^2
take square root of both sides of this equation to get:
r = 30
We want to find what v/pi equals.
since v = (4/3) * pi * r^3, and since r = 30, we get:
v = (4/3) * pi * (30)^3 which becomes:
v = (4/3) * pi * 27000
divide both sides of this equation by pi to get:
v/pi = (4/3) * 27000 = 36000.
our answer is:
v/pi = 36000
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