Q. 105.0( 1 Vote )

# Mark the correct alternative in the following:

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

A. 54π cm^{2}/min

B. 7π cm^{2}/min

C. 27 cm^{2}/min

D. none of these

Answer :

The lateral surface area of a cone, with radius r and height h, is defined as

-(1)

Given that r=7cm, h=24cm, and , we have to calculate

Differentiating (1) with respect to t, we get

Substituting values, we get

Simplifying above equation, we get

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