1. Find the volume of the solid obtained by rotating the region bounded by the given curves about the y-axis.
$x = \sqrt{r^2 - y^2}$
$y = -r, y = r$
What shape is the resulting object after rotating about the y-axis? Does the volume you calculated correspond to any known formulas? Make sure you setup the integral, show your antiderivative calculation, and do not use decimals.
2. The linear density $\rho$ in a rod 7 meters long is $\frac{9}{\sqrt{x + 9}}$ kg/m, where x measures in meters from one end of the rod. Find the average density of the rod in kg/m. Make sure to indicate how you set up the problem and what calculus you used.
