Answer
a) $6075 \pi $ and b) $19085 \space ft^2$
Work Step by Step
Our aim is to integrate the integral to compute the surface area. In order to solve the integral, we have:
a) $Surface \space Area(S_A)= (2 \pi)\int_{a}^{b} y \sqrt {1+(\dfrac{dy}{dx})^2}$
or, $ =(2 \pi)\int_{-22.5}^{45} \sqrt {R^2-x^2} \times \dfrac{R}{\sqrt {R^2-x^2}} dx =(2 \pi ) \int_{-22.5}^{45} R dx= 6075 \pi$
b) The required nearest square foot $6075 \pi \approx 19085 \space ft^2$
