Problem $7\mathrm{.}6\mathrm{.}9$

A solid spherical ball of magnesium alloy $)$ is lowered into the ocean to a depth of $8000$ ft $.$ The diameter of the ball is $9\mathrm{.}0$ in $.$

$($a$)$ Determine the decrease $d$ in diameter, the decrease $V$ in volume, and the strain energy $U$ of the ball.

$($b$)$ At what depth will the volume change be equal to $0\mathrm{.}0324\%$ of the original volume?