1.26: Figure 3 shows a right triangular prism .

Figure 3 shows a right triangular prism $\displaystyle ABCDEF$. A cross section $\displaystyle ABC$ of the prism is a triangle in which $\displaystyle AB = AC = r\mathrm{cm}$ and $\displaystyle \angle CAB = \frac{\pi}{3}$ radians.

In the prism

(a) Show that the volume of the prism is $\displaystyle \frac{5\sqrt{3}}{4} r^2 \mathrm{cm}^3$

The volume of the prism is increasing in such a way that the size of $\displaystyle \angle CAB$ and the size of $\displaystyle \angle DEF$ remain constant and the length of $\displaystyle AE$, the length of $\displaystyle BF$ and the length of $\displaystyle CD$ remain constant.

The lengths of $\displaystyle AB$, $\displaystyle AC$, $\displaystyle ED$ and $\displaystyle EF$ are each increasing at a constant rate of $\displaystyle 0.2\mathrm{cm}/\mathrm{s}$

(b) Find the exact rate of increase, in $\displaystyle \mathrm{cm}^3/\mathrm{s}$, of the volume of the prism when the area of the rectangular face $\displaystyle BCDF$ is $\displaystyle 60\mathrm{cm}^2$