1. ## Related Rate problem

The problem is:

An inverted cone is being filled up with water at a rate of 100cm^3/s

The cone is 60 cm high and the radius is half of the height.

At what rate is the depth increasing if the height of the water is 10cm?

The answer I got is: 1.27cm/s

Can someone tell me if I am correct?

And the height of the cone is not needed if you're given that the radius is half the height right?

Thank you

2. Volume of cone: $V=\frac{\pi}{3}r^{2}h$

Since the height is 60, the radius is 30.

We can skip the similar triangles since we were told that $r=\frac{h}{2}$

That gives $V=\frac{h^{3}{\pi}}{12}$

$\frac{dV}{dt}=\frac{{\pi}h^{2}}{4}\cdot\frac{dh}{d t}$

Now, plug in all your knowns and solve for dh/dt

YOU ARE CORRECT. Except maybe keep in your answer in the form $\frac{4}{\pi}$

3. Sweet (: Thank you

And yeah Ill keep it in
$

\frac{4}{\pi}
$