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(A) The volume $V$ of a spherical balloon is given by $V = \frac{4}{3} \pi r^3$.Differentiating both sides with respect to time $t$,we get:$\frac{dV}{

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$1/\pi \ cm/sec$

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(A) The volume $V$ of a spherical balloon is given by $V = \frac{4}{3} \pi r^3$.Differentiating both sides with respect to time $t$,we get:$\frac{dV}{dt} = 4 \pi r^2 \frac{dr}{dt}$.Given that $\frac{dV}{dt} = 900 \ cm^3/sec$ and the radius $r = 15 \ cm$,we substitute these values into the equation:$900 = 4 \pi (15)^2 \frac{dr}{dt}$.$900 = 4 \pi (225) \frac{dr}{dt}$.$900 = 900 \pi \frac{dr}{dt}$.Solving for $\frac{dr}{dt}$:$\frac{dr}{dt} = \frac{900}{900 \pi} = \frac{1}{\pi} \ cm/sec$.Thus,the radius of the balloon is increasing at a rate of $1/\pi \ cm/sec$.

$A$ balloon,which always remains spherical,is being inflated by pumping in $900 \ cm^3/sec$ of gas. Find the rate at which the radius of the balloon is increasing when the radius is $15 \ cm$.

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