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Question

If the volume of a spherical balloon is increasing at the rate 900cm3/sec, then the rate of change of radius of balloon instant when radius is 15 cm [in cm/sec]


A

227

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B

22

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C

722

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D

None of these

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Solution

The correct option is C

722


Explanation for the correct option :

Find the rate of change of radius,

The volume of the sphere is given as V=43πr3.

Now differentiate the equation with respect to time:

dVdt=43π·3r2drdtdVdt=4πr2drdt

Now the rate of change of volume is 900cm3/sec, so dVdt=900.

Then the rate of change of radius when r=15 cm is given as:

900=4π×152drdt900=900πdrdt900900π=drdt1π=drdt

Now taking the value of π as 227 the rate of change is:

drdt=1227drdt=722

Hence, the correct option is C.


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