Water is poured at a constant rate of $20\,\mathrm{c}{{\mathrm{m}}^{3}}$ per second into a cup which

Question

Water is poured at a constant rate of $20\,\mathrm{c}{{\mathrm{m}}^{3}}$ per second into a cup which is shaped like a truncated cone as shown in the figure. The upper and lower radii of the cup are $4\,\mathrm{cm}$ and $2\,\mathrm{cm}$ respectively. The height of the cup is $\mathrm{6}\,\mathrm{cm}$. Show that the volume of water inside the cup, $V$ is related the height of the water level, $h$ through the equation $V\,=\,\frac{\pi }{27}{{(h=6)}^{3}}-8\pi $ [3] How fast will the water level be rising when $h$ is $\mathrm{3}\,\mathrm{cm}$? Express your answer in exact form. [3]

Accepted Answer

$A = 2kp$, $B = \frac{40}{9}\pi k$; $r = \left(\frac{9p}{20\pi}\right)^{1/3}$; $H : r = 4 : 1$

2007 AJC P1 Q13

2007 AJC P1 Q13

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