Question

The area of cross-section of a pipe is \[5.4{\text{ c}}{{\text{m}}^2}\] and water is pumped out of it at the rate of \[27{\text{ km/h}}\]. Find in liters the volume of water that flows out of the pipe in one minute.

Answer 1

Hint: Here we will be using the formula of calculating volume which equals the product of the area of the base to its height. The formula is shown below:
\[{\text{Volume}} = {\text{Area of base}} \times {\text{height}}\]

Complete step-by-step answer:
Step 1: As the area of the pipe given in the question is in the form of centimeters then first we will be converting the rate of water pumped out of the pipe or we can say the height of the pipe into centimeter per minute form from kilometer per hour as shown below:
\[27{\text{ km/h = 27}} \times {\text{100000 cm/60 minutes}}\]
(\[1{\text{ km}} = 100000{\text{ cm}}\] and
\[1{\text{ hour}} = 60{\text{ min}}{\text{.}}\])
By solving the above expression, we get:
\[ \Rightarrow 27{\text{ km/h = 45000 cm/min}}\]
Step 2: Substituting the values of
\[{\text{Area of base = 5}}{\text{.4 c}}{{\text{m}}^2}\] and
\[{\text{Height = 45000 cm}}\] into the formula of volume
\[{\text{Volume}} = {\text{Area of base}} \times {\text{height}}\] we get:
\[ \Rightarrow {\text{Volume}} = 5.4 \times 45000\]
By replacing the term,
\[5.4 = \dfrac{{54}}{{10}}\] in the above expression we get:
\[ \Rightarrow {\text{Volume}} = \dfrac{{54}}{{10}} \times 45000\]
By dividing the RHS side of the above expression with \[10\] we get:
\[ \Rightarrow {\text{Volume}} = 54 \times 4500\]
After doing the multiplication in the RHS side of the above expression we get:
\[ \Rightarrow {\text{Volume}} = 2430000{\text{ c}}{{\text{m}}^3}\]
Step 3: By converting the volume from centimeter to liters, first we will convert it into meters as shown below:
\[ \Rightarrow {\text{Volume}} = 24300{\text{ }}{{\text{m}}^3}\]
(\[1{\text{ cm}} = 100{\text{ m}}\])
Now after converting the volume in liters from meter cube we get:
\[ \Rightarrow {\text{Volume}} = 24300000{\text{ L}}\]
(\[1{\text{ }}{{\text{m}}^3} = 1000{\text{ L}}\])
So, we can say that water releasing per minute is \[24300000{\text{ L/min}}{\text{.}}\]

\[\because \] The volume of the water is \[24300000{\text{ L}}\].

Note:
Students need to remember the conversion units for solving these types of questions. Some of them are shown below:
\[1{\text{ }}{{\text{m}}^3} = 1000{\text{ L}}\]
\[1{\text{ cm}} = 100{\text{ m}}\]
\[1{\text{ km}} = 100000{\text{ cm}}\]
\[1{\text{ hour}} = 60{\text{ min}}{\text{.}}\]