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Question

Gas is being pumped into a spherical balloon at the rate of 30ft3min. Then the rate at which the radius increases when it reaches the value 15ft is


A

130πftmin

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B

115πftmin

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C

120πftmin

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D

125πftmin

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Solution

The correct option is A

130πftmin


Step 1. Given Data,

Spherical balloon pumped at the Rate dVdt=30ft3min(where, V is the volume of sphere.)

Radius r=15ft

Step 2. We have to calculate the rate of increase of radiusdrdt,

We know that,

Volume of Sphere V=43πr31

Differentiating equation 1 with respect to time t we get,

dVdt=43π3r2drdtdVdt=4πr2drdt2

Putting the given value in the equation 2 we get,

dVdt=4πr2drdtdrdt=14πr2dVdtdrdt=14π15ft230ft3mindrdt=130πftmin

Hence, the rate of increase of radiusdrdt=130πftmin.

Hence, option A is correct.


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