Question

Construct an iterated integral to determine the volume of the solid over the cardioid r =
1+cosq between the plane z = 0 and the cone z = r.

Answer 1

The region is bounded by\[0\le\theta\le2\pi\]\[0\le r\le1+\cos\theta\]and z si bounded by\[0\le z\le r\]and \(dV\) for cylindrical coordinates is\[dV=rdzdrd\theta\]now all you have to do is execute\[\int\int\int dV\]on the prescribed bounds to find the volume