SOLUTION: A sphere is just inclosed inside the right circular cylinder. If the volume of the gap between cylinder & sphere is 90 cm cube.Find the volume of the sphere.

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Question 1104361: A sphere is just inclosed inside the right circular cylinder. If the volume of the gap between cylinder & sphere is 90 cm cube.Find the volume of the sphere.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A sphere is just inclosed inside the right circular cylinder.
If the volume of the gap between cylinder & sphere is 90 cm cube.
Find the volume of the sphere.
:
cylinder vol - sphere vol = 90
(pi%2Ar%5E2%2Ah) - (4%2F3*pi%2Ar%5E3) = 90
The radius of the base of the cylinder and the radius of the sphere are the same
The height of the cylinder = the diameter of the sphere or 2r
(pi%2Ar%5E2%2A2r) - (4%2F3*pi%2Ar%5E3) = 90
(pi%2A2r%5E3) - (4%2F3*pi%2Ar%5E3) = 90
factor out pi%2Ar%5E3
pi%2Ar%5E3(2+-+4%2F3) = 90
pi%2Ar%5E3(2%2F3) = 90
multiply both sides b6 3
2%2Api%2Ar%5E3 = 270
divide both sides by 2
pi%2Ar%5E3 = 135
r = 3sqrt%28135%2Fpi%29
find the cube root
r = 3.5026 cm
:
Find the vol of the sphere
V = (4%2F3*pi%2A3.5026%5E3)
V = 180 cu/cm
:
The vol of the cylinder will be 270 cu/cm, interesting relationship!
see if that checks out
pi%2A3.5026%5E2%2A7.0052 = 269.99, pretty close