Consider the region between the graph of f(x)=x−2 and the x-axis on [2,4]. For the line of rotation given below, use a definite integral to find the volume of the resulting solid.

Question

Around the line x=7

The volume of the solid is___________?

PLEASE show work!! STEP BY STEP!!!

Answer 1

Draw a figure!

The radius of revolution is 7-(x-2) = 9-x

The volume of each slice is 2π(9-x) dx and

The volume of the solid is ∫ 2π∫(9-x)dx between 2 and 4.

This is a simple integral and I will leave it to you to evaluate.

P.S.

The solid is the bottom portion of a cone and you can, if you wish, check your result by knowing the formula for the volume of a cone.