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Question

A spherical balloon is filled with 4500πcumof helium gas. If a leak in the balloon causes the gas to escape at the rate of 72πcum/min, then the rate (inm/min) at which the radius of the balloon decreases 49min after the leakage began is


A

97

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B

79

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C

29

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D

92

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Solution

The correct option is C

29


Explanation for the correct option:

Step 1. Volume of balloon; V=43πr3 …..(1)

After 45 minutes, Volume =4500π-4972π

=972π …..(2)

Step 2. Equate equation (1) and (2):

43πr3=972π

r3=729

r=9

Step 3. Differentiate the volume of balloon with respect to r:

V=43πr3

dVdt=43π.3r2drdt

72π=4πr2drdtdVdt=72π

drdt=724r2

drdt=72492

drdt=29

The radius of the balloon 29m/min decreases.

Hence, Option ‘C’ is Correct.


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