# How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #y=f(x)=3x-x^2# and x axis revolved about the x=-1?

##### 1 Answer

#### Explanation:

Imagine a cylindrical shell as a rectangular prism with width

The volume of the cylindrical shell is width x length x thickness (height)

Now width

If we sketch the parabola

Also, the radius of the cylindrical shell is considered to be the distance from the axis of revolution

Hence, r

i.e. the change in volume,

To find the volume, we limit the thickness of the shells, and find their summation within the domain