## Thomas' Calculus 13th Edition

$\frac{64\pi^3}{27}$
We calculate the area as follows: $A=\int^{2\pi}_0 \int^{4\theta/3}_0 rdr d\theta$ =$\frac{8}{9}\int^{2\pi}_0 \theta^2 d\theta$ =$\frac{64\pi^3}{27}$