Question

a swimming pool has to be drained for maintenance. the pool is shaped like a cylinder with a diameter of 6 m and a depth of 1.1 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? use the value 3.14 for π, and round your answer to the nearest hour. do not round any intermediate computations. hour(s)

Explanation:

Step1: Calculate the radius of the pool

The diameter of the pool is \(d = 6\space m\), so the radius \(r=\frac{d}{2}=\frac{6}{2}=3\space m\).

Step2: Calculate the volume of the cylindrical pool

The formula for the volume of a cylinder is \(V=\pi r^{2}h\). Given \(\pi = 3.14\), \(r = 3\space m\), and \(h=1.1\space m\).
Substitute the values into the formula: \(V=3.14\times3^{2}\times1.1\).
First, calculate \(3^{2}=9\). Then \(V = 3.14\times9\times1.1=3.14\times9.9 = 31.086\space m^{3}\).

Step3: Calculate the time to empty the pool

The rate of pumping is \(13\space m^{3}\) per hour. Use the formula \(t=\frac{V}{rate}\).
Substitute \(V = 31.086\space m^{3}\) and rate \(= 13\space m^{3}/h\). So \(t=\frac{31.086}{13}\approx2.39\).

Answer:

\(2\)