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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 1.7 m. Suppose water is pumpedinto the pool at a rate of 16 m³ per hour. How many hours will it take to fill the empty pool?Use the value 3.14 for x, and round your answer to the nearest hour.

1 Answer

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First, we need to find the volume of the pool.

Use the cylinder volume equation:


V=\pi r^2h

where:

r= radius

h = height

To find the radius r=d/2, then r=9m/2 = 4.5m.

and the height is the depth = 1.7

Replace using the equation:


\begin{gathered} V=\pi(4.5m)^2(1.7m) \\ V=(3.14)(4.5m)^2(1.7m) \\ V=108.09m^3 \end{gathered}

Hence, the pool holds 108.09m³ of water, at a rate of 16m³/hr.


(108.09m^3)/(16(m^3)/(hr))=7hr

It will take 7 hours to fill the empty pool (The answer is rounded to the nearest hour)

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