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5.5 Application of double integrals

1.

(a) $\displaystyle{\frac{3\pi}{4}}$ (b) $\displaystyle{9(\frac{\pi}{12} - \frac{\sqrt{3}}{8})}$ (c) $\displaystyle{2\pi}$

2.

(a) $\displaystyle{2\pi}$ (b) $\displaystyle{\frac{3\sqrt{3}}{2}}$ (c) $\displaystyle{\frac{2\pi}{3}\left((a^{2} + 1)^{3/2} - 1\right)}$

3.

(a) $\displaystyle{\pi}$ (b) $\displaystyle{\frac{\pi}{2}}$