Q.

A spherical iron ball 10 cm in radius is coated with a layer of ice of  uniform thickness that melts at a rate of   when the thickness of ice is 5 cm than the rate at which the thickness of ice decreases.

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a

590π  cm/min

b

905π cm/min

c

95π cm/min

d

90π cm/min

answer is A.

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Detailed Solution

V  =​​43 πr3dVdt=4πr2drdt50=4π(15)2drdtdrdt=50900π=590πcm/min
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A spherical iron ball 10 cm in radius is coated with a layer of ice of  uniform thickness that melts at a rate of   when the thickness of ice is 5 cm than the rate at which the thickness of ice decreases.