An inverted conical water tank has a radius of 10 m at the t

[kimmy_koo51]

An inverted conical water tank has a radius of 10 m at the top and 24 m high. If water flows into the tank at a rate of 20 m ^3/min, how fast is the depth of the water increasing when water is 16m deep?

Nothing! I got Nothing! I have a test tomorrow! ARGH!~!

 

[stapel]

Nothing! I got Nothing!

I would guess that you are expected to know the volume formula for a cone, so start by memorizing that:

The volume V of a right-circular cone with radius r and height h is given by V = (1/3)(pi)(r²)(h).

What can you do with that?

Eliz.

 

[kimmy_koo51]

Well....since its calculas...differentiate it?

 

[galactus]

You can't just differentiate the volume of a cone. You have 2 variables, kimmy koo. You need to eliminate 1 of them. You need dh/dt, so we'll eliminate r and differentiate with respect to h. See?.

\(\displaystyle V=\frac{1}{3}{\pi}r^{2}h\)

Use similar triangles:

\(\displaystyle \L\\\frac{r}{h}=\frac{10}{24}\)

\(\displaystyle \L\\r=\frac{5}{12}h\)

Now, sub that into your cone volume formula along with your given data, differentiate and solve for dh/dt.

 

[kimmy_koo51]

9/20PI m/min....?

 

[galactus]

Very good.

 

[kimmy_koo51]

Thanks a mil!