How do I calculate the rate of water being pumped into an inverted conical tank?

[rkennedy9064]

I need help understanding a problem for my homework assignment. I'm not sure how to set up the problem. If anyone could help I would greatly appreciate it.

Homework Statement

Water is being pumped into an inverted conical tank at a constant rate. However, water is also leaking out of the tank at a constant rate of 0.01m^3/min. The tank is 6m tall and the radius at the top of the tank is 2 m. If the water level is rising at a rate of 0.2m/min at the moment when the height of the water is 2m, find the rate at which water is being pumped into the tank.

Homework Equations

The Attempt at a Solution

I know I need to find the rate of change, but I'm not sure how exactly I set up this problem.

 

[tiny-tim]

welcome to pf!

hi rkennedy9064! welcome to pf!

call the height of the water y(t), the volume of water w(y), and the pumping rate p

then write an equation for dw/dt …

what do you get? ​

 

[HallsofIvy]

Do you know the formula for the volume of a cone with height h and base radius r?

You will want to reduce from two variables, h and r, to only one- either h or r. You can do that by seeing that for the entire tank r= 2 while h= 6 and the cone formed by the water maintains that shape (think "similar triangles").