# Cylindrical Shells Volume

1. Oct 13, 2011

### silverbell

1. The problem statement, all variables and given/known data

Using cylindrical shells, find the volume obtained by rotating the region bounded by the given curves about the x-axis.

x= (y^2) +1

x= 0

y=1

y=2

2. Relevant equations

2∏ ∫ rh

3. The attempt at a solution

2∏ ∫ from 1 to 2 (y^2) + 1

2. Oct 13, 2011

### Staff: Mentor

Start with a sketch of the region that is being rotated. Then draw a sketch of the solid that is formed.

3. Oct 13, 2011

### silverbell

I drew a sketch. I'm not sure what do do about the radius part. I know y= 2 is the higher radius along the x-axis. And y= 1 is the lower radius along the x-axis. Do I subtract the radius minus function?

4. Oct 13, 2011

### Staff: Mentor

The expression for incremental volume (the volume of a thin horizontal strip that is revolved around the x-axis) is 2$\pi$ * radius * width of strip * Δy.

The radius varies from what to what?
How wide is a typical strip?