1. ## Rates of Change

A conical reservoir has a depth of 24 feet and a circular top of radius 12 feet. It is being filled so that the depth of water is increasing at a constant rate of 4 feet per hour. Determine the rate in cubic feet per hour at which water is entering the reservoir when the depth is 5 feet.

I'm still knew to the whole finding rates of change thing but I know I'm suppose to find the derivative of the Volume, but I don't know how to deal with the equation afterward. Help?

2. Originally Posted by ment2byours
A conical reservoir has a depth of 24 feet and a circular top of radius 12 feet. It is being filled so that the depth of water is increasing at a constant rate of 4 feet per hour. Determine the rate in cubic feet per hour at which water is entering the reservoir when the depth is 5 feet.

I'm still knew to the whole finding rates of change thing but I know I'm suppose to find the derivative of the Volume, but I don't know how to deal with the equation afterward. Help?

dh/dt=4 , the question wants dv/dt when h=5

dv/dt=dv/dh x dh/dt , using the chain rule .

V=pir^2h
From here , we can find dv/dh

Now , we hv got everything , just sub into the above equation .

3. what happens to dr/dt?

4. Originally Posted by ment2byours
what happens to dr/dt?

It isn't required . dh/dt is given in the question but not dr/dt