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?"
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I keep doing the math for it and get 359 cubed inches (rounded to the closest whole number) when including the pi, and 114*pi cubed inches when I exclude it. The answer choices are 60*pi cubed inches, 65*pi cubed inches, 85*pi cubed inches, and 90*pi cubed inches. Can someone go through the math of this?

Answer 1

Large cone:

V = 1/3 x pi x r^2 x h

= 1/3 x 3.14 x 9^2 x 15

= 1272.3 cubic inches

Smaller cone:

V = 1/3 x pi x r^2 x h

= 1/3 x 3.14 x 3^2 x 5

= 47.1 cubic inches 

1272.3 - 47.1 = 1225.2 cubic inches

1272/3.14 ≈ 390

The answer is 390 × pi.