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.
+128460 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
