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Q.

A spherical iron ball of radius 10cm is coated with a layer of ice of uniform thickness that melts a rate of 50cm3/min When the thickness of the ice 5cm, then the rate at which the thickness (in cm/min) of the ice decreases, is:

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a

56π

b

136π

c

19π

d

118π

answer is B.

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Detailed Solution

dvdt=50     r-15 V=43πr3  ⇒  dvdt=4πr2 drdt                    ⇒ 50=4π×15+15+drdt                    ⇒ drdt=118π

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