A shell method (calculus) question?

[jcfor3ver]

Homework Statement

Heres the question.
Use shell method to find volume:

y=3+2x-x^2 with boundaries: y=0, x=0, intercept x=3 and rotate around x=4

Homework Equations

I know that V=2pi (integral from 0 to 3) (radius)*(height) dx

The Attempt at a Solution

My radius was (4-x) and my ht was y=3+2x-x^2

now my answer was aprox= 155.51, and i triple checked it. What the hell am I doing wrong because it seems like that volume is much too large for an answer. my exact answer was 99/2pi

 

[vela]

You didn't do anything wrong. Your answer is correct. Your intuition is off.

To get a really rough estimate of what the volume should be, try approximating the shape as a flat disk of radius 4 with a hole of radius 1 in the middle. If you plot y vs. x, you can see 3 would be a decent approximation for the height of this flat disk. If you calculate the volume of the disk, it comes out to 47π, which is pretty close to the exact volume you found.