$[12$ points$]$ Sketch the solid whose volume is calculated by the triple integral, and find the volume:

${\displaystyle \underset{\frac{}{4}}{\overset{\frac{}{2}}{}}}{\displaystyle \underset{0}{\overset{}{}}}{\displaystyle \underset{0}{\overset{3}{}}}{}^{2}sinddd$

Hint: The shape is part of a sphere.

If you are having difficulty sketching, you can provide an attempt that clearly shows the bounds in each variable and then describe an everyday object that the shape looks like to you.

$5.[16$ points$]$ Find the volume between the surfaces $z=8-x^2-y^2$ and $z=x^2+y^2.$

Hints: Use desmos to guide you in setting up the integration.

You can most easily use either a double polar integral or a triple cylindrical integral. You will need to find the intersection of the two surfaces to get your limits of integration.

Please help with #$4,5$ and show all work with the sketch. Thank you