A company manufactures a hallow cylinder component that is closed at the end. The r=4" & h=8". To make each cylinder 42 pi cubic inches of material is needed. 1. Write a function to express the volume of the material needed. 2. Write an equation than can be solved to find the required thickness of the component.

Question

A company manufactures a hallow cylinder component that is closed at the end. The r=4" &  h=8". To make each cylinder 42 pi cubic inches of material is needed. 1. Write a function to express the volume of the material needed. 2. Write an equation than can be solved to find the required thickness of the component.

oobleck · Accepted Answer

you need to specify the thickness of the material, and assuming that the end cap is the same thickness t, and the inner radius is 4, then the volume is
πt(4+t)^2 + π((4+t)^2-4^2)*8 = πt^3 + 16πt^2 + 80πt
= πt(t^2 + 16t + 80)
so to find t, just solve
πt^3 + 16πt^2 + 80πt = 42π
t^3 + 16t^2 + 80t - 42 = 0
t = 0.48 in

adjust things if the outer radius was 4", rather than the inner radius

Mish · Answer

Thank you!