Related Rate Problem

[tfeuerbach]

How would one go about solving this problem:

Given that the height of a cylinder is always twicer its radius, find the rate of change of the volume of the cylinder when the volume is 16pi cm^3 and its radius is changing at 4 cm/sec.

 

[stapel]

How would one go about solving this problem:

Given that the height of a cylinder is always twicer its radius, find the rate of change of the volume of the cylinder when the volume is 16pi cm^3 and its radius is changing at 4 cm/sec.

What is the formula for the volume V of a cylinder, in terms of its height h and its radius r? What expression states this particular height in terms of this particular radius? How does this edit the general formula for the volume?

What is stated as changing? At what is it changing? So what derivative equation does this give you?

When this particular volume is 16pi, what then is the radius value?

What rate of change are you asked to find? What equation should then be differentiated? Plugging in the known values (volume, radius, and the one given rate of change), what do you get for the requested rate of change?

If you get stuck, please reply showing all of your work so far. Thank you.