Question

Set up but do not solve an integral to find the volume of the ice cream cone. The ice cream is the upper hemisphere of the unit circle and the cone has height 3 (the vertex is: (r,z) = (0,-3), so below the xy-plane).

Answer 1

Area of circle is pir^2
\[V_{cone} = \pi \int\limits_{-3}^0 (1 + \frac{z}{3})^{2} dz\]

Answer 2

\[V_{\top} = \pi \int\limits_0^1 (1-z^{2})^{2} dz\]