Finding the Volume of a Rotated Arch Dam Using the Shell Method

[Sentral]

Homework Statement

I need to find the volume of an arch dam that is rotated 150 degrees. The problem can be found at this link: http://college.cengage.com/mathematics/larson/calculus_early/2e/students/downloads/mws6a.pdf" and it is number 4.

I know the axis of rotation is 150 and the rotation is 150 degrees.

Homework Equations

I'm pretty sure I will need to use the shell method. I'm also sure I will need to translate the equations 220 units to the right. So I get $$.03x^2-6.1x+240$$ for the interval 150 <= x <=204. 389 on the interval 204 < x < 220. And $$-6.593x+1839.46$$ on 220 <= x <= 279.

The Attempt at a Solution

I have many attempts at the solution, but everytime I try I seem to get different answers, that I don't feel are correct. For example, I split the cross section into 3 parts. Which are 2 triangle looking shapes, and a rectangle. The problem says the axis of rotation is at 150. So the shell method I do $$2pi*int(x(.03x^2-6.1x+240))$$ and evaluate it for a=150 and b=204. Then I would multiply this number by (150/360) since it's only 150 degree rotation. Would I just do this for each of the sections?

 

[lippyka]

Can someone please help me understand what I'm doing wrong and how to solve this problem correctly? Any help would be appreciated. Thank you!