Chapter 15 - Multiple Integrals - 15.3 Double Integrals in Polar Coordinates - 15.3 Exercises - Page 1055: 19

$V$ = $\frac{625\pi}{2}$

$V$ = $\int\int{x^2+y^2}dA$ $V$ = $\int_0^{2\pi}\int_0^5r^3drdθ$ $V$ = $\frac{1}{4}\int_0^{2\pi}[r^4]_0^{5}dθ$ $V$ = $\frac{1}{4}\int_0^{2\pi}625dθ$ $V$ = $\frac{625}{4}[θ]_0^{2\pi}$ $V$ = $\frac{625\pi}{2}$