You have to apply the chain rule when differentiating.
Your h should be when r=2
So just plug in your values. and solve for
I have tried this problem, but it's not working out.
Sand poured on the ground at a rate of 3 meters cubed per minute forms a conical pile whose height is 1/3 the diameter of the base. How fast is the altitude increasing when the radius of the base is 2 m.
First I replace r in the conical V=1/3 PIE r^2h
I take h = 1/3 d
h=1/3(2r)
So I get r = 3h/2
So then I put it in V=1/3 PIE (3h/2)^2h
When I do the derivative I get
dV/dt=3PIEh^2 dh/dt
I plug in the numbers
3=3PIE(2)^2 dh/dt
and get .0795 m/min
But the answer is .239m/min
What am I doing wrong in this problem, if someone can help thanks.
Joanne
I am a bit lost here. Why is it 9/12 PIE h^3?? I have tried to figure it out and it's not working.
grrrrrrrrrr on not getting it
Jo
UPDATE here is what I got and finally got the answer at plugging at it for a while.
h=1/3(2r)
From this I got h=4/3 and r =3h/2
Then V=1/3Pi(3h/2)^2h
V=1/3 Pi (9h/4)^3
dV/dt=1/3 Pi(27/4)h^2 dh/dt
3=1/3 Pi(27/4)(4/3)^3
dh/dt = 0.239 m/min
I was shocked myself when I got it.
I could not figure yours out above, the way you did it.