Question

an empty swimming pool needs to be filled to the top. the pool is shaped like a cylinder with a diameter of 8 m and a depth of 1.7 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: Calculate the radius of the pool

The diameter \(d = 8\) m, so the radius \(r=\frac{d}{2}=\frac{8}{2}=4\) m.

Step2: Calculate the volume of the cylindrical pool

The formula for the volume of a cylinder is \(V=\pi r^{2}h\). Given \(r = 4\) m, \(h=1.7\) m, and \(\pi = 3.14\). Then \(V=3.14\times4^{2}\times1.7\).
First, \(4^{2}=16\). Then \(V = 3.14\times16\times1.7\).
\(3.14\times16 = 50.24\), and \(50.24\times1.7=85.408\) \(m^{3}\).

Step3: Calculate the time to fill the pool

The rate of filling is \(11\) \(m^{3}\) per hour. Using the formula \(t=\frac{V}{r}\) (where \(V\) is volume and \(r\) is rate), \(t=\frac{85.408}{11}\).
\(\frac{85.408}{11}=7.76436\cdots\)

Answer:

\(8\) hours (rounded to the nearest hour)