Question

a swimming pool has to be drained for maintenance. the pool is shaped like a cylinder with a diameter of 5 m and a depth of 1.3 m. suppose water is pumped out of the pool at a rate of 13 m³ per hour. if the pool starts completely full, how many hours will it take to empty the pool? do not round any intermediate computations. round your answer to the nearest hour. use the value 3.14 for π.

Explanation:

Step1: Find the radius of the pool

The diameter is 5 m, so radius $r = \frac{5}{2} = 2.5$ m.

Step2: Calculate the volume of the pool

Volume of cylinder $V = \pi r^2 h$. Using $\pi = 3.14$, $r = 2.5$ m, $h = 1.3$ m:
$V = 3.14 \times (2.5)^2 \times 1.3 = 3.14 \times 6.25 \times 1.3 = 25.5125$ $m^3$.

Step3: Find time to drain the pool

Time = Volume / Drain rate = $\frac{25.5125}{3} \approx 8.504$ hours, rounded to nearest hour is 9.

Answer:

9