1
$\begingroup$

If E is the region of space located inside the sphere $x^2 + y^2 + z^2 = 4$ and below the cone $z = \sqrt{3x^2 + 3y^2}$

How may I describe E in cylindrical and spherical coordinates? And how may I use E to evaluate:

\begin{equation*} \int\int\int_{E} z^2 dV \end{equation*}

I'm stuck, so any tip will be helpful

Thanks in advance!

$\endgroup$
  • 1
    $\begingroup$ Begin by converting the given equations to the cylindrical coordinate system. $\endgroup$ – user147263 Oct 6 '14 at 3:53
  • $\begingroup$ "Below the cone" - Do you mean "inside the cone"? $\endgroup$ – user_of_math Oct 6 '14 at 5:09
  • $\begingroup$ @user_of_math No, I really meant below or under the cone. Inside the sphere and under the cone. $\endgroup$ – user78723 Oct 6 '14 at 11:37
0
$\begingroup$

In spherical coordinates, E can be described by $0\le\theta\le 2\pi, \;\;0\le\rho\le2, \;\;\frac{\pi}{6}\le\phi\le\pi$.

In cylindrical coordinates, I believe E can be described by $0\le\theta\le2\pi$ and

for $0\le r\le1, \;\;-\sqrt{4-r^2}\le z\le\sqrt{3}r$

for $1\le r\le2, \;\;-\sqrt{4-r^2}\le z\le\sqrt{4-r^2}$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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