Set up and evaluate the indicated triple integral in the appropriate coordinate system. Enter an exact
answer. Do not use a decimal approximation.
$\iiint_Q z \,dV$, where $Q$ is the region between $z = \sqrt{x^2 + y^2}$ and $z = \sqrt{16 - x^2 - y^2}$
$\iiint_Q z \,dV =$
Evaluate the iterated integral after changing coordinates systems. Enter an exact answer. Do not use a
decimal approximation.
$\int_0^3 \int_0^{\sqrt{9-y^2}} \int_{\sqrt{x^2+y^2}}^{\sqrt{18-x^2-y^2}} 2 \,dz \,dx \,dy =$
Convert the spherical point $(\rho, \phi, \theta)$ into rectangular coordinates.
$(8, \pi, 0)$
Write your answer in exact form and in terms of $\pi$.
Use an appropriate coordinate system to find the volume of the given solid.
The region inside $z = \sqrt{3x^2 + 3y^2}$ and between $z = 4$ and $z = 6$
$V = $
