+4622 The volume of a cylinder is 60 cubic centimeters. What is the number of cubic centimeters in the volume of the sphere it circumscribes?
+129899 Call the radius of the cylinder and sphere, r
And the height of the cylinder = 2r
So
60 = pi * r^2 * 2r
30 = pi * r^3
30/pi = r^3
[30/pi]^1/3 = r
So...the volume of the sphere is
(4/3)pi [ (30/pi)^1/3 ]^3 =
(4/3) pi * 30/pi =
40 cm^3
We could also see this by the forllowing ratio
Vsphere = (4/3)pi *r^3 (4/3) 4 2 40
_______ __________ = _____ = ______ = __ = ___
V cylinder pi * r^2 * 2r 2 6 3 60
