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Question

A spherical iron ball of radius 10 cm is coated 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 at which the thickness (in cm/min) of the ice decreases, is:

A
136π
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B
56π
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C
118π
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D
19π
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Solution

The correct option is C 118π

Let the thickness of ice as h cm, then the volume of spherical ball is
dVdt=4π(10+h)2dhdt
50=4π(10+5)2dhdt
dhdt=118πcmmin( signify the decrease in thickness)

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