A student in Chennai fills a spherical balloon with a foot pump that delivers 120 cm³ of air every…

Step 1. The radius. $120 = 4\pi \times 100 \times \dfrac{dr}{dt}$, so $\dfrac{dr}{dt} = \dfrac{120}{400\pi} = 0.0955\ \text{cm/s}$.

Step 2. The surface area. $\dfrac{dS}{dt} = 8\pi r\,\dfrac{dr}{dt} = 8\pi \times 10 \times 0.0955 = 24\ \text{cm}^2/\text{s}$.