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Question

Find the rate of change of the total surface area of a cylinder of radius r and height h, when the radius varies.


Solution

Let T be the total surface area of a cylinder. Then,

T = 2πrr+h

Since the radius varies, we differentiate the total surface area w.r.t. radius r.

Now,

dTdr=ddr2πrr+hdTdr=ddr2πr2+ddr2πrhdTdr=4πr+2πhdTdr=2πr+h

Mathematics
RD Sharma XII Vol 1 (2015)
Standard XII

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