# A water tank has the shape of an upside-down cone with radius 2 m and height 5 m. The water is running out of the tank through a small hole at the bottom. What is the rate of change of the water level when flow-out reads #3 m^3/min# at height, #h= 4 m#?

##### 1 Answer

rate of change is

#### Explanation:

We are given the rate of change of volume

and are asked to find the rate of change of water level ,

In terms of a differential equation we can express this as

**equation1**

we want to find

The volume of a cone is given by

And in this case

Substituting this into the Volume equation gives:

We can now differentiate:

When h = 4, then

So if we substitute this back into equation 1: