Gas is being pumped into a spherical balloon at the rate of 30ft3/min Then the rate at which the radius increases when is reaches the value 15 ft,  is

# Gas is being pumped into a spherical balloon at the rate of $30{\mathrm{ft}}^{3}/\mathrm{min}$ Then the rate at which the radius increases when is reaches the value  is

1. A

$\frac{1}{30\pi }\mathrm{ft}/\mathrm{min}$

2. B

$\frac{1}{15\pi }\mathrm{ft}/\mathrm{min}$

3. C

$\frac{1}{20}\mathrm{ft}/\mathrm{min}$

4. D

$\frac{1}{25}\mathrm{ft}/\mathrm{min}$

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### Solution:

Let be the radius of the spherical balloon and

be the volume at any time $t$.

It is given that  $\frac{dV}{dt}=30f{t}^{3}/\mathrm{min}$

Now, $V=\frac{4}{3}\pi {r}^{3}$

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