Question

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.

Answer 1

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.

$\frac{108.09m^3}{16\frac{m^3}{hr}}=7hr$

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