You would be correct if were a constant.
However, is a function dependent on . The correct derivative is therefore
Hope this helps.
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?