Question

An empty swimming pool needs to be filled to the top. The pool is shaped like a cylinder with a diameter of 10m and a depth of 1.7 m. Suppose water is pumped into the pool at a rate of 12 m^3 per hour. How many hours will it take to fill the empty pool? Use the value 3.14 for pie and round your answer to the nearest hour. Do not round any intermediate computations

Answer 1

Given data:

An empty swimming pool needs to be filled to the top. The pool is shaped like a cylinder with a diameter of 10m, and a depth of 1.7m.

The water is pumped into the pool at a rate of 12 meter cube per hour.

The formula for the volume of a cylinder is

`V=\pi r^2h`

where,

`\begin{gathered} d=10m\Rightarrow r=5m \\ h=1.7m \end{gathered}`

Thus,

`\begin{gathered} V=\pi(5)^2*1.7 \\ =3.14*5*5*1.7 \\ =133.45m^3 \end{gathered}`

At a rate of 12 meter cube per hour.

`\begin{gathered} =(133.45m^3)/(12(m^3)/(hr)) \\ =11.12\text{ hours.} \end{gathered}`

It will take 11.12 hours to fill the empty pool