Question

cylindrical coordinates help!

Answer 1

Sketch the solid whose volume is given by

Answer 2

\[\int\limits_{0}^{\pi/6}\int\limits_{0}^{\pi/2}\int\limits_{0}^{3} \rho ^{2} \sin \theta d \rho d \theta d \phi\]

Answer 3

what does this thing look like??

Answer 4

You mean spherical coordinates! lol!

Answer 5

yes, i do!

Answer 6

Can you check if there was not a typo for sin phi instead of sin theta.
The Jacobian for dV calls for a rho^2sin phi drho dtheta dphi.

Answer 7

If it is sin(phi), then it is a thirty-degree quarter open cone 3 units in radius opening towards the north pole, and situated in the first octant.

Answer 8

you're right, it was sin phi

Answer 9

how did you get the thirty degree part of that?

Answer 10

OH phi is measured from the top! I get you now.

Answer 11

great, thanks!

Answer 12

You're welcome!