Answer
(a) $A=400sin\theta cos\theta=200sin2\theta$
(b) See graph.
(c) width=$14.14cm$, depth=$14.14cm$
Work Step by Step
(a) Use the figure given in the exercise, with diameter $D=20cm$ and the angle shown in the figure, we have width=$Dcos\theta=20cos\theta$, depth=$20sin\theta$, thus the cross sectional area $A=20cos\theta\times20sin\theta=400sin\theta cos\theta=200sin2\theta$
(b) See graph.
(c) Based on the graph, a maximum of the area ($200cm^2$) can be found at $\theta=\frac{\pi}{4}$ which gives
width=$20cos\frac{\pi}{4}=14.14cm$, depth=$20sin\frac{\pi}{4}=14.14cm$
