- Draw the region in space described by the bounds of the integral $$ \int_{0}^{\pi}\int_{0}^{\pi/6}\int_{0}^{5}\rho^2\sin \phi d\rho d\phi d\theta.$$
- Use a triple integral with spherical coordinates to find the volume of a hemiball of radius $7$ (so the region under the sphere $x^2+y^2+z^2=7^2$ and above the $xy$-plane). Note that $dV=\rho^2\sin\phi d\rho d\phi d\theta$ in spherical coordinates. Actually compute the integral you set up.
- Set up the integral from #2 in cylindrical coordinates.
- Now find the centroid of the hemiball in #2.
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