Applications of Partial Derivatives-Cone

[mit_hacker]

[SOLVED] Applications of Partial Derivatives-Cone

Homework Statement

(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?

Homework Equations

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)
However, I do not know how to proceed from here on. Please help me.

 

[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.

 

[mit_hacker]

!

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

 

[mit_hacker]

Thanks a lot!

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