Problem Value: $1$ point$($s$).$ Problem Score: $88\%.$ Attempts Remaining: $19$ attempts.

Help Entering Answers

$(1$ point$)$ Express the volume of the solid enclosed by the cone $z=\sqrt[\phantom{2}]{x^2+y^2}$ and the sphere $x^2+y^2+z^2=32$ with a triple

integral in cylindrical coordinates.

NOTE: When typing your answers use $"$th$"$ for $.$

Volume $={\displaystyle \underset{{}_1}{\overset{{}_2}{}}}{\displaystyle \underset{r_1}{\overset{r_2}{}}}{\displaystyle \underset{z_1}{\overset{z_2}{}}}$

$dzdrd$

$z_1=$

$z_2=\sqrt[\phantom{2}]{32-r^2}$

$r_1=$

$r_2=$

${}_1=$

${}_2=$

Evaluate the integral

Volume $=(256(\sqrt[\phantom{2}]{2}-1))\frac{}{3}$

If you don't get this in $3$ tries, you can see a similar example $($online$).$ However, try to use this as a last resort or after you have

already solved the problem. There are no See Similar Examples on the Exams!

Hint: