3. A balloon that blows up in the shape of a perfect cube is being blown up at a rate such that at time $t$ fortnights, it has surface area $6 t$ square furlongs. At how many cubic furlongs per fortnight is the air being pumped in when the surface area is 144 square furlongs?
Solution: The surface area at time $t$ is $6 t$, so the volume is $t^{3 / 2}$. Hence the air is being pumped in at a rate of $\frac{3}{2} \sqrt{t}$. When the surface area is $144, t=24$, so the answer is $3 \sqrt{6}$.