How Do You Calculate the Correct Radius for Cylindrical Shells?

[kazafire93]

Homework Statement

Hi, I'm having a tremendous amount of difficulty with finding the radii in problems using cylindrical shells.

Here's the question: find the volume of the solid found by rotating the region bounded by the given curves:

x = y²+1, x = 2, about y = -2

I got 2 - (y²+1) for the height, which I know is correct. For the radius, though, I got 1 + y...which is incorrect. Can anyone explain how to get the right answer? Thanks!

 

[SammyS]

Homework Statement

Hi, I'm having a tremendous amount of difficulty with finding the radii in problems using cylindrical shells.

Here's the question: find the volume of the solid found by rotating the region bounded by the given curves:

x = y²+1, x = 2, about y = -2

I got 2 - (y²+1) for the height, which I know is correct. For the radius, though, I got 1 + y...which is incorrect. Can anyone explain how to get the right answer? Thanks!

Hello kazafire93. Welcome to PF !

If you were rotating about y = -1, the radius of the cylindrical shell would be y - (-1) = y + 1.

But you're rotating about y = -2.