Rate of change problem?

[kayla765]

Okay, I have an extra credit problem that I have an answer to, but I really need to get this right haha

The height and radius of a right circular cone are each increasing at 2 cm/sec. Find the rate at which the volume is increasing when the radius is 6 cm and the height is 4 cm. V= (1/3)(pi)r^2h

I'm just not sure what to do with having the radius and height. I only know what to do when I have one of them!

I have this for the derivative of the volume equation- (1/3)((r^2)(dh/dt) + h(2r(dr/dt))), and then I have dh/dt= 2 and dr/dt= 2, but I'm not sure what to do next? Thanks!

 

[arthur ohlsten]

V=1/3 pi R^2 H

Find the rate of change of the V,[dV/dt] when H=4cm and R=6 cm.
dR/dt =2 cm/sec
dH/dt=2 cm/sec
dV/dt = [pi/3] [H(2R dR/dt)+R^2 dH/dt]
dV/dt=[pi/3][4(12)(2) +36(2)]
dV/dt = [pi/3][96+72]
dV/dt=[pi/3[168]
dV/dt= 56 pi cm cubed per sec.


Please check for errors

Arthur

 

[kayla765]

Ah, thank you so much! You were right