Question

Cal Help! Involves rate of change!

Answer 1

The height and radius of an expanding right circular cone are always equal, and the volume of the cone is increasing at the rate of 2 cubic inches per minute. How fast is the radius growing?

Answer 2

The derivative is rate of change, so I would need the derivative of the formula of volume, which is 1/3pi(r^2)h.....I just don't know what to do with that XD

Answer 3

well, notice that your problem said that the height and radius are the same or equal

Answer 4

this means that the actual equation should be:

dv/dt=(pi)r^2*dr/dt

Answer 5

now, we are also told that that the rate at which the volume of the cone is increasing is : 2 cubic inches. Thus we can rewrite the problem as:

2=pi*r^2*dr/dt

Answer 6

now simply isolate dr/dt

Answer 7

So would it be dr/dt=2/pi*r^2?

Answer 8

boy that looks good to me

Answer 9

Thank you sir!