4.03: Related rates in a cone
Water is poured into an inverted cone. The semi-vertical angle is \(30^\circ\) and \(\tan30^\circ=1/\sqrt3\).
(a)[2]
Show that the volume of water of depth \(h\) is \(V=\dfrac{\pi}{9}h^3\).
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(b)[4]
Given \(\dfrac{\mathrm dV}{\mathrm dt}=50\), find \(\dfrac{\mathrm dh}{\mathrm dt}\) when \(h=60\), giving the answer in terms of \(\pi\).
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