E-RC02 · A conical water surface
Water fills a cone in which the surface radius and depth satisfy \(\displaystyle r= \frac{h}{3}\). The inflow is \(10\pi\ \mathrm{cm^3\,s^{-1}}\). Use \(\displaystyle V=\frac13\pi r^2h\).
Express V in terms of h only and find \(\displaystyle \frac{dV}{d}h\).
Find the rate of increase of depth and of surface radius when \(\displaystyle h=6 \mathrm{cm}\).
Find the rate of increase of the area of the horizontal water surface at the same instant.
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