Question

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.

          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.

1. Find the volume of the solid obtained by rotating the region bounded by the given curves about the y-axis.
x = √(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 ρ in a rod 7 meters long is (9)/(√(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.

Added by Tracey A.

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