Question

A solid machine part is to be manufactured as shown in the figure The part is made by cutting a small cone off the top of a larger cone The small cone has a base radius of 3 inches and a height of 5 inches. The larger cone has a base radius of 9 inches and had a height of 15 inches prior to being cut What is the volume of the resulting part illustrated in the fiqure?

Answer 1

The exact volume of the part is 390pi in.^3

Using pi = 3.14, the approximate volume of the part is 1224.6 in.^3

Explanation:

Find the volume of the large cone and the volume of the small cone. The subtract the small volume from the large volume.

Large cone:

V = (1/3)(pi)r^2h

V = (1/3)(pi)(9 in.)^2(15 in.)

V = 405pi in.^3

Small cone:

V = (1/3)(pi)r^2h

V = (1/3)(pi)(3 in.)^2(5 in.)

V = 15pi in.^3

Difference in volumes:

volume of part = 405pi in.^3 - 15pi in.^3 = 390pi in.^3

The exact volume of the part is 390pi in.^3

Using pi = 3.14, the approximate volume of the part is 1224.6 in.^3