Thread: Triple Integral in Cylindrical Coordinates

1. Triple Integral in Cylindrical Coordinates

Find the mass of a ball B given by $x^2+y^2+z^2 \leq a^2$ if the density at any point is proportional to its distance from the z-axis.

I figured that $\rho=Kr$, so the integrand would be $Kr^2$. I think that my limits of integration are wrong. I got $0\leq\theta\leq2\pi$, $0\leq r \leq a$, $-\sqrt{a-r^2} \leq z \leq \sqrt{a-r^2}$

2. Originally Posted by MathTooHard
Find the mass of a ball B given by $x^2+y^2+z^2 \leq a^2$ if the density at any point is proportional to its distance from the z-axis.

I figured that $\rho=Kr$, so the integrand would be $Kr^2$. I think that my limits of integration are wrong. I got $0\leq\theta\leq2\pi$, $0\leq r \leq a$, $-\sqrt{a-r^2} \leq z \leq \sqrt{a-r^2}$
The limits on z are incorrect...but you're very close. I'll give you a chance to see if you can spot your mistake. If you can't, reply back, and I'll help you.

3. Oh wow, I can't believe I spent that much time agonizing over this problem. Thanks!

4. wouldn't spherical be easier?

5. It would indeed. I should have mentioned that my textbook specifically wanted cylindrical coordinates.