# How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #y=5x^2#, y=5x revolved about the x-axis?

##### 1 Answer

Please see below.

#### Explanation:

In order to use shells, we need to take our representative slice parallel to the axis of rotation. So we will take a horizontal slice at a value of

Below is a partial picture. The curves intersect at

The horizontal slice is shown in black and the radius of revolution is the dotted black line. Its length is

The volume of a representative shell is

In this problem,

The greater

We need to rewrite the equation

The lesser

So the reprentative shell has volume

Details omitted

# = (5pi)/3#