# Math Help - rate question

1. ## rate question

I haven't seemed to get rate problems down yet. Can anyone help me with this one?

water is poured into a conical funnel at a rate of 1cm"3 per second. The radius of the top of the funnel is 10cm and the height of the funnel is 20cm. Find the rate at which the water level is rising when it is 5cm from the top of the funnel.

FYI (The formula for the volume of a cone is V=1/3 Pir"2h)

2. Use similar triangles to eliminate a variable.

$\frac{r}{h}=\frac{10}{20}$

$r=\frac{1}{2}h$

Sub into your volume formula and differentiate with respect to time.

$V=\frac{1}{3}{\pi}(\frac{1}{2}h)^{2}h=\frac{1}{3}{ \pi}\frac{h^{3}}{4}$