# Applications of Partial Derivatives-Cone

1. Oct 24, 2007

### mit_hacker

[SOLVED] Applications of Partial Derivatives-Cone

1. The problem statement, all variables and given/known data

(Q) (Q) If a cone grows in height by dh/dt = 1 and in radius by dr/dt = 2, starting from zero, how fast is its volume growing at t =3?

2. Relevant equations

3. The attempt at a solution

By applying the chain rule for partial derivatives, I obtained:

∂V/∂t=(2/3 πrh)(dr/dt)+(1/3 πr^2 )(dh/dt)

2. Oct 24, 2007

### EnumaElish

1. Your left hand side should be dV/dt, not partial V/partial t
2. If h increases 1 unit/sec. and r increases 2 units/sec., what would h be in 3 seconds? What would r be in 3 secs.?
3. Now that you know what h(3) and r(3) are, you can substitute those values along with dh/dt and dr/dt to find dV/dt.

3. Oct 24, 2007

### mit_hacker

!!!

Ahhhh! Why didn't I see it? It was such a simple thing.

4. Oct 24, 2007

### mit_hacker

Thanks a lot!

Sorry I forgot to mention in my last post. Thanks a lot for your help!!!