Question

The area of cross-section of a pipe is $5.4c{m^2}$ and water is pumped out of it at the rate of 27km/h. Find in litres the volume of water which flows out of the pipe in one minute.

Answer 1

Hint:
We will convert the units of the area of a cross-section in square metre and the rate of flow of water in metres/minute because we want to find the volume of water in litres flowed in one minute and $1{m^3} = 1000{\text{Litres}}$. Then, multiply the area of the cross-section and the rate of flow of water to find the volume of water in litres.

Complete step by step solution:
We are given that the cross-section of the pipe is $5.4c{m^2}$ and the rate of flow is 27km/hr
We know that the volume of the water that flows out of the pipe is the product if the cross=section and the rate of flow.
But, the units have to be same.
Here, the area of cross-section is in $c{m^2}$ and the rate of flow is in km/h.
Also, we are required to find the volume of water that flowed out in litres.
Therefore, we will convert both the given quantities in metres because $1{m^3} = 1000{\text{Litres}}$
Now, we have to divide $5.4c{m^2}$ by $100 \times 100$ to convert into ${m^2}$
Therefore, the area of the cross-section of the pipe is $\dfrac{{5.4}}{{100 \times 100}}{m^2}$
Similarly, we will multiply the 27km/h by 1000 to convert the unit to metres.
Hence, the rate if flow is $27 \times 1000$m/h
But, we want to find the amount of water flowed in I minute.
And there are 60 minutes in 1 second.
Therefore, divide $27 \times 1000$ m/h by 60 to determine the rate of flow in one minute.
That is, rate of flow of water from pipe is $\dfrac{{27 \times 1000}}{{60}}m/\min $
Now, as we know the product of the area of cross-section of the pipe and the rate of flow gives the total volume of the water that flows out of the pipe.
Therefore, the volume will be,
$\dfrac{{5.4}}{{100 \times 100}} \times \dfrac{{27 \times 1000}}{{60}}{m^3} = \dfrac{{5.4 \times 27}}{{600}}{m^3}$
Also, $1{m^3} = 1000{\text{Litres}}$
$\dfrac{{5.4 \times 27}}{{600}} \times 1000{m^3} = 243{m^3}$

Therefore, the volume of the water that flowed out is 243 litres.

Note:
Conversion of units plays an important role in this question. Students must remember the formulas, such as $1m = 100cm$, $1km = 1000m$ and $1{m^3} = 1000{\text{litres}}$ to avoid errors. Also, we have not solved the fractions initially, as after getting multiplied many of the terms got cancelled and calculations became less time-consuming.