# calculus: related rates

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A cylindrical can is being heated with its height increasing at the rate of 0.01cm/min and its diameter at the rate of 0.005cm/min. At what rate is the volume increasing when the can has a diameter of 15cm and a height of 20cm.

this is how i'm going about the question. I have to find dv/dt. my known variables (i think) are dh/dt=0.01 and ddiam/dt=0.005. and i'm using the equation V=(pi)r^2 * h

I've never done a question before where i was given two rates before, can you please tell me how to go about this question? the solution is 4.123~cm^3/min

and just a little side question. let's say i'm given the rate for the increasing diameter. (as in the question is 0.005cm/min) can i divide that by 2 to get the rate of increasing radius?

Thank you so much for your time

• calculus: related rates -

V= PI r^2 * h

dv/dt= PI (2rh dr/dt+ r^2 dh/dt)

you are given dh/dt, dr/dt. Find dv/dt when those are given, and given r and h.

• calculus: related rates -

:O Thank you so much, for some reason i totally forgot about the product rule! hahah... :)

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