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 5 inches and had a height of 12 inches prior to being cut. What is the volume of the resulting part illustrated in the figure?

Answer 1

So then we do
large-small

V=(1/3)hpir^2

given
small=r=3 and h=5
V=(1/3)5pi3^2
V=5pi3
V=15pi

large, r=5, h=12
V=(1/3)5pi12^2
V=5pi48
V=240pi


large-small=240pi-15pi=225pi in^3

aprox 706.8582 in^3