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Q.

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

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a

118π

b

136π

c

56π

d

154π

answer is A.

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Detailed Solution

Let thickness =x cm Total volume V=43π(10+x)3dVdt=4π(10+x)2dxdt Given dVdt=-50 cm3/min At x=5 cm, we get -50=4π(10+5)2dxdtdxdt=-118πcm per min

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