SOLUTION: 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 ?

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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