Answer
a) $6075 \pi$
(b) $19085 \space ft^2$
Work Step by Step
a) The formula to determine the surface area is as follows:
$S= \int_{m}^{n} 2 \pi y \sqrt {1+(\dfrac{dy}{dx})^2} \\= 2 \pi \times \int_{-22.5}^{45} \sqrt {R^2-x^2} \times \dfrac{R}{\sqrt {R^2-x^2}} dx \\=(2 \pi ) \int_{-22.5}^{45} \space R \space dx \\= 6075 \pi$
b) We need the required nearest square foot $6075 \pi \approx 19085 \space ft^2$
