# Find The Volume of A Solid

1. Dec 1, 2011

### andromeda92

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

find the volume of the solid bounded by the graphs of the given equations:

r=1+cos∅
z=y
z=0
(the first octant)

2. Relevant equations

V=$\int$$\int$ rdrd∅

3. The attempt at a solution

So, I've been having trouble deciding what to integrate from and to. I converted the z equations into polar coordinates, so, z=rsin and z=0

$\int$$^{2\pi}_{0}$$\int$$^{1+cos∅}_{0}$ (rsin)rdrd∅

Mod note: revised LaTeX
$$\int_0^{2\pi} \int_0^{1 + cos(\theta)} rsin(\theta) r~dr~d\theta$$

I found, from the first integration, [2∏]\int[/0][itex] r^(3)sin∅/3 d∅ and I need to plug in (1+cos∅) and 0 for r....but, this seems WAY too complicated having a trig function to the 3rd power.

I'm not even sure if I have the beginning correct. Can anyone help me out?

Last edited by a moderator: Dec 1, 2011
2. Dec 1, 2011

### Astronuc

Staff Emeritus
In three dimensions, the first quadrant has x ≥ 0, y ≥ 0, z ≥ 0, and think about the limits of ∅ for x ≥ 0, y ≥ 0.