+468 A right cylinder with a base radius of 3 units is inscribed in a sphere of radius 5 units. The total volume, in cubic units, of the space inside the sphere and outside the cylinder is W*pi. Find W, as a common fraction.
+130071 Sphere volume = (4/3) pi (5)^3 = 500/3 pi
(1/2) the height of the cylinder is given by sqrt [ 5^2 - 3^2 ] = sqrt (16) = 4
So....the total height = 8
Cylinder volume = pi * (3^2) * ( 8) = 72 pi
Volume outside the cylinder but inside the sphere = pi [ 500 / 3 - 72 ] =
[ 500 - 216 ] / 3 * pi = [284/3] pi
So W = 284 / 3
