解: (1)在Rt△ABF中,AB=4<span class="zgs">$\sqrt {3}$</span>,∠A=30°,BF=2<span class="zgs">$\sqrt {3}$</span>。OB=4,∠BOD=120°,扇形OBD面积<span class="zgs">$\frac{120\pi\times4^2}{360}=\frac{16\pi}{3}。$</span>
(2)弧长$\frac{120\pi\times4}{180}=\frac{8\pi}{3},$底面半径$\frac{8\pi}{3}\div2\pi=\frac{4}{3}。$