(i)[3]
Show that, for a water depth of $h\,\text{cm}$ in the tank, the water volume, $V\,\text{cm}^3$, is given by $V = (40\sqrt{3})h^2$.
(ii)[3]
Find the rate at which $h$ is increasing when $h = 5$.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
Fig. 1 illustrates an open tank formed as a triangular prism. The two vertical ends $ABE$ and $DCF$ are congruent isosceles triangles. $
angle ABE = \angle BAE = 30^\circ$. $AD$ has length $40\,\text{cm}$. The tank is held so that the top $ABCD$ lies horizontally. Water is added at a steady rate of $200\,\text{cm}^3\,\text{s}^{-1}$. If the water depth is $h\,\text{cm}$ after $t$ seconds from the start of filling, this is shown in Fig. 2.