Finding the Volume of Two Solids: A Cylindrical Approach

[tifa8]

Hello I need help for this problem, it has been 4 hours trying to do it

Homework Statement

Find the volume of the region of space above the xy-plane, inside the cone z=7−\sqrt{x^{2}+y^{2}} and inside the cylinder x^{2}+y^{2}=4x.

Homework Equations

The Attempt at a Solution

I tried to switch to cylindrical coordinates and I got

0\leq\theta\leq2\pi
0\leqr\leq4cos(\theta)
0\leqz\leq7-r

so,
V=\int^{2\pi}_{0}\int^{4cos(\theta)}_{0}\int^{7-r}_{0}rdzdrd\theta
which doesn't work...

thanks in advance

 

[SammyS]

I think you'll find that θ goes from -π/2 to π/2 .

 

[tifa8]

thank you

 

[lramsa1]

I think you'll find that θ goes from -π/2 to π/2 .

How did you find these bounds?