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Q.

Water is being filled at the rate of 1cm3/sec in a right circular conical vessel (vertex downwards) of height 35 cm and diameter 14 cm. When the height of the water level is 10 cm, the rate ( in cm2 / sec ) at which the wet conical surface area of the vessel increases is

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a

 265

b

 2610

c

 5

d

 215

answer is C.

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Detailed Solution

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From figure rh=735h=5r

Question Image

Volume of the cone =V=13πr2h

dVdt=1ddtπr2h3=1

ddt5π3r3=1r2drdt=15π

Let wet conical surface area =S

=πr=πrh2+r2 =26πr2dSdt=226πrdrdt

When h =10 then r =2 dSdt=22610

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