Thread: Related rates problem

First, I want to say I am terrible with word problems... here is the problem:
Sand falling from a hopper at a rate of 10pi ft^3/sec forms a conical pile whose radius is always equal to half its height. How fast is the radius of the pile increasing when the radius is 5ft.

I believe the equation is V = (1/3)*pi*r^2*h
here is what I know:

the derivative of the equation is: (2/3)pi*rh

r = (1/2)h = 5
h= 2r = 10

To plug all this in (2/3)pi (5)(10)

= (100/3)pi

=104.7198 ft^2/ sec

Is this right?

You would be correct if were a constant.

However, is a function dependent on . The correct derivative is therefore



Hope this helps.

That being said, then it would be:
(2/3)pi(5^2)

= (50/3)pi

which turns out to be 52.3599 ft/sec?

Not quite. We are given that



When , this becomes

I think I see what you are trying to say now. Get dr/dt on one side so it will be:

10pi/50pi = .2 ft/sec?

That is correct.