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Question

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

A
56π
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B
154π
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C
136π
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D
118π
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Solution

The correct option is D 118π
Let thickness of ice be x cm.
Therefore, net radius of sphere =(10+x) cm

Volume of sphere V=43π(10+x)3

dVdt=4π(10+x)2dxdt
At x=5,dVdt=50 cm3/min
50=4π×225×dxdt
dxdt=118π cm/min

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