Chapter 15 - Multiple Integrals - 15.3 Double Integrals in Polar Coordinates - 15.3 Exercises - Page 1055: 20

$V$ = $\frac{14\pi}{3}$

$V$ = $\int_0^{2\pi}\int_1^2\sqrt {r^2}rdrdθ$ $V$ = $\int_0^{2\pi}\int_1^2{r^2}drdθ$ $V$ = $\frac{1}{3}\int_0^{2\pi}[r^3]_1^2dθ$ $V$ = $\frac{1}{3}\int_0^{2\pi}[8-1]dθ$ $V$ = $\frac{1}{3}\int_0^{2\pi}7dθ$ $V$ = $\frac{7}{3}[θ]_0^{2\pi}$ $V$ = $\frac{14\pi}{3}$