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

@mani_jha!

Answer 2

So phi goes from 0 to 2Pi to make a cardioid, r goes from 0 to 1+cos(phi) to fill in the cardioid's surface and height z goes from 0 to r. Then just include the jacobian for polar coordinates (r) and presto:
\[\int\limits_{0}^{2\pi} d \phi \int\limits_{0}^{1+\cos \phi}r dr \int\limits_{0}^{r}dZ\]

Also the answer is 5pi/3.