Question

A rectangular swimming pool has a length 30 meters, width of 10 meters and average depth is 2 meter. If a hose can fill the pool at a rate of 0.5 cubic meter per minute, how many hours will it take to fill the pool?
A. 12 hours
B. 24 hours
C. 20 hours
D. 15 hours

Answer 1

Hint: First of all we have to imagine a diagram of a rectangular pool. Then to find the amount of water contained in the pool, we have to calculate the volume of a rectangular pool by this formulae \[v=l\times b\times h\text{ }{{\text{m}}^{3}}\]. After getting the volume we have to calculate the time as a hose can fill the pool at a rate of 0.5 cubic meters per minute. After getting the time in minutes we have calculated it in an hour so that we can conclude our question.

Complete step-by-step answer:

Here is a diagram of a rectangular swimming pool.
The swimming pool has a length \[l=30\] meters, width of \[b=10\] meters and average depth is \[h=2\] meter.
We know the volume of a rectangular pool is \[v=l\times b\times h\text{ }{{\text{m}}^{3}}\] where “l” is length, “b” is width, “h” is height and “v” is volume of the pool.
Now putting the value of \[l=30\] meters, \[b=10\] meters, \[h=2\] meter we get,
\[\begin{align}
  & \Rightarrow v=30\times 10\times 2\text{ }{{\text{m}}^{3}} \\
 & \Rightarrow v=600\text{ }{{\text{m}}^{3}} \\
\end{align}\]
The volume of the rectangular pool is \[600\text{ }{{\text{m}}^{3}}\].
Now according to the question a hose can fill the pool at a rate of 0.5 cubic meters per minute.
\[0.5\text{ }{{\text{m}}^{3}}\]pool will be filled in 1 minute
\[\text{1 }{{\text{m}}^{3}}\] pool will be filled in
\[\begin{align}
  & \dfrac{1}{0.5}\text{ minute} \\
 & \Rightarrow \text{2 minute} \\
\end{align}\]

Now, time will take to fill the \[600\text{ }{{\text{m}}^{3}}\] pool will be,
\[\begin{align}
  & 600\times 2\text{ minute} \\
 & \Rightarrow \text{1200 minute} \\
\end{align}\]
We know to convert minute to hour we have divided the minute value with 60.
Now converting the value from minute to hour we get,
\[\begin{align}
  & \dfrac{\text{1200}}{60}\text{ hour} \\
 & \Rightarrow 20\text{ hour} \\
\end{align}\]
To fill the rectangular pool the hose will take 20 hour (Option C).

Note: To find the amount of water in the pool students has to calculate the volume of the pool. So they have to remember the formula of volume of a volume of a rectangular pool is \[v=l\times b\times h\text{ }{{\text{m}}^{3}}\]. In this problem we can directly write the time taken using the concept of rate.
It is given that rate of filling the pool is \[0.5\text{ }{{\text{m}}^{3}}/\min \]
Now we have to find the time.
So we can divide the total volume \[600\text{ }{{\text{m}}^{3}}\] by \[0.5\text{ }{{\text{m}}^{3}}/\min \] so that the unit of the answer we get will be in minutes. Then we can convert it to hours.
\[\begin{align}
  & \dfrac{600}{0.5} \\
 & \Rightarrow \dfrac{6000}{5} \\
 & \Rightarrow 1200 \\
\end{align}\]
The pool will fill in 1200 min. Which is,
\[\begin{align}
  & \dfrac{1200}{60} \\
 & \Rightarrow 20 \\
\end{align}\]
The hose will take 20 hours to fill the swimming pool.