# Finding volume of arch dam

1. Oct 5, 2009

### Sentral

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

The axis of revolution is 150 and the rotation is 150 degrees.

2. Relevant equations

Using the shell method.

My offset is x+220.

The equations that make up the cross section:

$$.03x^2+7.1x+350$$

$$-6.593x+389$$

$$389$$

3. The attempt at a solution

I planned on splitting the cross section into three parts, which are the 2 triangles and rectangles, and apply the shell method on each of these. So first I did $$2pi*Integral[(x+220)(.03x^2+7.1x+350)]$$ with the bounds being -70 to -16. Then I multiplied this answer by (150/360) since it's only 150 degree rotation. In each of my applications of the shell method, the p(x), or the distance to the axis of revolution stayed at x+220. Am I on the right track if I do this for each of the 3 sections?

2. Oct 8, 2009

### tiny-tim

Welcome to PF!

Hi Sentral! Welcome to PF!

(have a pi: π and an integral: ∫ and try using the X2 tag just above the Reply box )

I'm not sure what you're doing (what's 220? ) …

the shell method involves finding the volume of the arc-shaped slice (it will be 150/360 of the volume of a complete cylinder) from x to x + dx …

it will be something times dx …

and then integrating.