Question

an empty swimming pool needs to be filled to the top. the pool is shaped like a cylinder with a diameter of 9 m and a depth of 1.8 m. suppose water is pumped into the pool at a rate of 11 m³ per hour. how many hours will it take to fill the empty pool? use the value 3.14 for π, and round your answer to the nearest hour. do not round any intermediate computations.

Explanation:

Step1: Find radius of cylinder

Radius $r = \frac{\text{diameter}}{2} = \frac{9}{2} = 4.5$ m

Step2: Calculate volume of pool

Volume $V = \pi r^2 h = 3.14 \times (4.5)^2 \times 1.8$
$= 3.14 \times 20.25 \times 1.8 = 3.14 \times 36.45 = 114.453$ m³

Step3: Find time to fill pool

Time $t = \frac{V}{\text{rate}} = \frac{114.453}{11.3} \approx 10.13 \approx 10$ hours

Answer:

10 hours