A cylinder is wight inches high with a radius of three inches. It contains a ball with a diameter of five inches. What volume is left unoccupied in the cylinder?

Complete Question

A cylinder is eight inches high with a radius of three inches.It contains a ball with a diameter of five inches. What volume is left unoccupied in the cylinder?

160.74 cubic inches

Step-by-step explanation:

Step 1

Find the volume of cylinder

= πr²h

A cylinder is eight inches high with a radius of three inches.

Height = 8 inches

Radius = 3 inches

Volume of the cylinder = π × 3² × 8

= 226.19 cubic inches

Step 2

Find the volume of sphere

= 4/3 π r³

It contains a ball with a diameter of five inches.

Diameter = Radius /2 = 5/2 = 2.5 inches

Volume of the Sphere = 4/3 × π × 2.5³

= 65.45 cubic inches

Step 3

What volume is left unoccupied in the cylinder?

This is calculated as:

Volume of Cylinder - Volume of sphere

= 226.19 cubic inches - 65.45 cubic inches

= 160.74 cubic inches

Therefore, the volume is left unoccupied in the cylinder is 160.74 cubic inches

rectangle: 9 1/8 x 4 1/9 = 37 37/72in

parallelogram: b times h= 10.3 x 6.2 = 63.86

trapezoid: a+b/2 times h= 42.5

volume of prism: l times w times h= 36