Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Use cylindrical coordinates to evaluate the triple integral $\iiint_E (x^2+y^2)dV$, where $E$ is the solid bounded by the circular paraboloid $z=16−4(x^2+y^2)$ and the $xy$-plane.

This is Homework. I dont know what to do. Please help so I can understand. Appreciate it.

share|improve this question
Do you know how to convert from Cartesian to cylindrical coordinates? –  Américo Tavares Mar 21 '13 at 22:00
As @AméricoTavares suggests, can you express each of $x$, $y$, and $z$ in terms of $r$, $\theta$, and $z$? –  Sammy Black Mar 21 '13 at 22:02

1 Answer 1

up vote 2 down vote accepted


  1. You want to express your region in terms of cylindrical coordinates $r, \theta, z$. That will determine the bounds of the integral.
  2. Use $x = r\sin \theta, y = r\cos \theta$ to convert $x^2+y^2$ to $r,\theta,z$ as well.
  3. Use $dV = rdrd\theta dz$ and integrate.
share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.