Vector Calculus I: Spring-2022
HW3 : Due Day 07 4/18

1. The slice of cake S0 4379S
   1. Write down a triple integral representing the volume of a slice of the cylindrical cake of height \(2''\) and radius \(5''\) between the planes \(\phi=\pi/6\) and \(\phi=\pi/3\). Evaluate this integral
   2. Where is the center of mass of the slice? (Assume constant density.)
2. The bead S0 4379S Suppose \(W\) is the region outside the cylinder \(x^2+y^2=1\) and inside the sphere \(x^2+y^2+z^2=2\). Calculate \[ Q = \int_W \left(x^2+y^2\right) \,dV \]
3. The cone (wrapup) S0 4379S After completing the cone activity, write down and evaluate a multiple (double or triple) integral for the volume of the cone.