The radius of a right circular cylinder is (3t +4)^(1/2) and its height is t^6 , where t is time in
seconds and the dimensions are in inches. Find the rate of change of the volume of the
cylinder, V,with respect to time, including the appropriate units.

Question

The radius of a right circular cylinder is  (3t +4)^(1/2) and its height is t^6 , where  t is time in 
seconds and the dimensions are  in inches. Find the rate of change of the volume of the 
cylinder, V,with respect to time, including the appropriate units.

moonlitfate · Answer

I know that the volume of a right cylinder is: V= pi*r^2*h

anonymous · Answer

You'll get V in terms of t, and then differentiate it with respect to t

moonlitfate · Answer

So plug in the give radius and height for r and h in the equation for volume, right?

moonlitfate · Answer

$$V = \pi(\sqrt{3t + 4})(t^{6})$$

moonlitfate · Answer

And I know that to differentiate it that you have to use the chain rule, but I've only done that with two functions.  How would you do it in this case since there are 3?

dan815 · Answer

its like this |dw:1363293063891:dw|