Thread: cylindrical coordinates = triple integral

1. cylindrical coordinates = triple integral

use cylindrical coordinates to find the centroid of the solid that is bounded above by the sphere x^2 +y^2 +z^2 =2 and below by the paraboloid z=x^2 +y^2.

Thank you very much.

2. You're breaking my heart, kc. You simply MUST be able to do this one.

Hint: $r^{2} = x^{2} + y^{2}$

Come on, show your stuff! You CAN do it.

3. TKHunny, I am not that great as you thought!

Luckily, I think I just solved this question. I have
r is from 0 to 1
theta is from 0 to 2 pi
z is from r^2 to sqrt(2-r^2)

V =[ (8sqrt(2)-7)pi]/6

By symmetry, x bar = y bar

z bar = 7/[16sqrt(2) -14]

therefore the centroid is (0,0,7/[16sqrt(2) -14] )

I hope that I am right since the answer is correct as the book given.

4. If only you had shown us how you found your limits for 'r', then it would have been almost perfect.
You also should have stated "x bar = y bar = 0". You left off the last part.

Now that you have done this one so well, who's right about whether or not you can do it?