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.

Guest Jan 1, 2019

#1**+2 **

Using the Pythagorean Theorem.....the height of 1/2 of the cylinder is

√[5^2 - 3^2] = √[16] = 4

So....the height of the whole cylinder = 8 units

The space between the sphere and the cylinder is given by :

Volume of sphere - Volume of cylinder =

(4/3)pi (radius of sphere)^3 - pi * (radius of cylinder)^3 * cylinder height =

pi [ (4/3)* 5^3 - (3)^2 * 8 ] =

pi [ 500 / 3 - 72 ] =

pi [ ( 500 - 216) / 3 ] =

pi [ 284 / 3 ]

So

W = 284 / 3

CPhill Jan 2, 2019