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?

Question

Kenna Foley

Mathematics

12 November, 12:45

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?

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Answers (1)

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Jakobe Cochran · 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