Homework Help: Finding the Centroid of a Solid

1. Oct 30, 2011

dancingmonkey

1. The problem statement, all variables and given/known data
Find the volume and the centroid of the solid E that lies above the cone z=√x^2+y^2 and below the sphere x^2+y^2+z^2=49.

2. Relevant equations

3. The attempt at a solution

My bounds were:
$\theta$=0 to 2$\pi$
$\varphi$=0 to $\pi$/4
$\rho$=0 to 7cos($\varphi$)

So my integral was:
∫∫∫p^2sin($\varphi$) d(rho) d$\varphi$) d(θ)

I just need help in if my bounds and integral are correct. If someone can help me with that, that would be great!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 30, 2011

LCKurtz

That last limit is wrong. What is the spherical coordinate equation of the sphere $\rho=?$

And of course, once you correct the limits, that formula just gives you the volume. I think you undertand there is more to do, right?

3. Oct 30, 2011

dancingmonkey

And yes I understand that I still have to solve the integrals :)

4. Oct 30, 2011

LCKurtz

What is the equation of the sphere in spherical coordinates? Your integral must go from ρ = 0 to ρ on the sphere. So you need the equation of the sphere in spherical coordinates. Hint: It is very simple!

5. Oct 30, 2011

dancingmonkey

So the equation of the sphere in spherical coordinates is ρ^2=x^2+y^2+z^2. So the integral should go from p=0 to 7, right?

6. Oct 30, 2011

LCKurtz

Yes! But actually the equation of the sphere in spherical coordinates is ρ = 7, not ρ = x2+y2+z2.

7. Oct 30, 2011

dancingmonkey

Ah! Ok I got it now, thank you so much for helping!