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: Find radius of cylinder

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

Step2: Calculate volume of pool

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: Compute time to empty

Time $t = \frac{V}{\text{rate}} = \frac{125.6}{14} \approx 8.97 \approx 9$? Wait, correction: Wait 3.14×25=78.5, 78.5×1.6=125.6; 125.6/14≈8.97→round to nearest hour is 9. Yes.
Wait final answer is 9 hours.

Step1: Calculate radius

$r = \frac{10}{2} = 5$ m

Step2: Find pool volume

$V = 3.14×5²×1.6 = 125.6$ m³

Step3: Compute empty time

$t = \frac{125.6}{14} ≈ 9$ hours

Answer:

11 hours