Problem
(6) A circular swimming pool has a diameter of \( 24 \mathrm{ft} \). and a water height of \( 3.5 \mathrm{ft} \). A pump can fill the pool at a rate of \( 1.2 \mathrm{ft}^{3} \) ( 9 gallons) per minute. About how long will it take to fill this pool (in hours)? (A) About 15 hours (B) About 1300 hours (C) About 88 hours (D) About 22 hours
Solution
Step 1 ：1. \(V_{cylinder} = \pi r^2 h\)
Step 2 ：2. \(V_{cylinder} = \pi (12)^2 (3.5) \approx 1587.4112 \mathrm{ft}^3\)
Step 3 ：3. \(t = \frac{V_{cylinder}}{1.2 \mathrm{ft}^{3}\mathrm{/ min}} \times \frac{1 \mathrm{hour}}{60 \mathrm{min}} \approx 22.065 \mathrm{hours}\)
