Question

a swimming pool has to be drained for maintenance. the pool is shaped like a cylinder with a diameter of 10 m and a depth of 1.6 m. suppose water is pumped out of the pool at a rate of 14 m³ per hour. if the pool starts completely full, how many hours will it take to empty the pool? use the value 3.14 for π, and round your answer to the nearest hour. do not round any intermediate computations.

Explanation:

Step1: Calculate radius of cylinder

Radius $r = \frac{\text{diameter}}{2} = \frac{10}{2} = 5$ m

Step2: Compute volume of cylinder

Volume $V = \pi r^2 h = 3.14 \times 5^2 \times 1.6 = 3.14 \times 25 \times 1.6 = 125.6$ m³

Step3: Find time to empty pool

Time $t = \frac{V}{\text{pumping rate}} = \frac{125.6}{112} \approx 1.13$ hours

Answer:

1.13 hours