(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

Answer

Expert–verified

Hide Steps

Answer

3. \(t = \frac{V_{cylinder}}{1.2 \mathrm{ft}^{3}\mathrm{/ min}} \times \frac{1 \mathrm{hour}}{60 \mathrm{min}} \approx 22.065 \mathrm{hours}\)

Steps

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. \(t = \frac{V_{cylinder}}{1.2 \mathrm{ft}^{3}\mathrm{/ min}} \times \frac{1 \mathrm{hour}}{60 \mathrm{min}} \approx 22.065 \mathrm{hours}\)

Answer

Popular Problems