Question $7$

$10$ pts

Convert the integral below from rectangular coordinates to both cylindrical and spherical coordinates, and evaluate the simpler iterated integral.

${\displaystyle \underset{0}{\overset{5}{}}}{\displaystyle \underset{0}{\overset{\sqrt[\phantom{2}]{25-x^2}}{}}}{\displaystyle \underset{0}{\overset{\sqrt[\phantom{2}]{25-x^2-y^2}}{}}}\sqrt[\phantom{2}]{x^2+y^2+z^2}dzdydx$

$\frac{125}{8}$

$\frac{625}{4}$

$625$

$\frac{625}{8}$