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Pena Washington
07/17/2023 · Elementary School

12. (3 points) A soccer ball is inflated at a rate of \( 5 \mathrm{~cm}^{3} / \mathrm{min} \). At what rate is the radius of the balloon increasing when the balloon has a radius of \( \frac{5}{2} \mathrm{~cm} \) ? The volume of a Sphere: \( V=\frac{4}{3} \pi r^{3} \) \( \begin{array}{ll}\text { (A) } \frac{1}{5 \pi} \mathrm{~cm} / \mathrm{min} & \text { (B) } 125 \pi \mathrm{~cm} / \mathrm{min} \\ \text { (C) } \frac{\pi}{5} \mathrm{~cm} / \mathrm{min} & \text { (D) } \frac{5}{\mathrm{~cm}} / \mathrm{min}\end{array} \)

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The rate at which the radius is increasing is \( \frac{1}{5 \pi} \, \text{cm/min} \).

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