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Question

The radius of the base of a cone is increasing at the rate of 3 cm/min and the altitude is decreasing at the rate of 4 cm/min. The rate of change of lateral surface when the radius is 7 cm and altitude is 24 cm is

A
54π cm2/min.
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B
7π cm2/min.
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C
27πcm2/min.
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D
none of these
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Solution

The correct option is C 54π cm2/min.
Slant height l2=r2+h2
l=25cm
Also,2ldldt=2rdrdt+2hdhdt
dldt=3cm/min
Surface Area of coneS=πrl
dSdt=π(rdldt+ldrdt)
dSdt=54πcm2/min

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