Question

The inner radius of a pipe is 2.1cm. How much water can 12 m of this pipe hold?

Answer 1

Hint: first of all, convert the height of the pipe to centimeters using the relation 1m = 100 cm. We know the formula of the volume of pipe, \[\text{Volume=}\pi {{r}^{2}}l\] . Now put the value of radius and length in the formula, \[\text{Volume=}\pi {{r}^{2}}l\] and get the volume.

Complete step-by-step answer:
Now, convert the volume into liters by using the relation \[1000c{{m}^{3}}=1liter\] and then, solve it further.

According to the question, it is given that the inner radius of the pipe is 2.1 cm. We have to get the quantity of water that 12 m of this pipe can hold.
The radius of the pipe = 2.1 cm …………………….(1)
The length of the given pipe = 12 m ………………………….(2)

We have to convert the unit of the given height in centimeters.

We know the relation between meter and centimeter, 1m = 100 cm ……………….(3)
Now, from equation (2) and equation (3), we get
The length of the given pipe = \[12\times 100cm=1200cm\] …………………..(4)
The pipe is in the shape of the cylinder.
We have the formula of volume of pipe, \[\text{Volume=}\pi {{r}^{2}}l\] ………………………(5)
Here, ‘r’ is the radius and ‘l’ is the length of the given pipe.
From equation (1) and equation (4), we have the radius and length of the given pipe.
Now, putting the value of the radius and length of the pipe in equation (5), we get,
\[\begin{align}
  & \text{Volume=}\pi {{r}^{2}}l \\
 & \Rightarrow \text{Volume=}\dfrac{22}{7}\times 2.1cm\times 2.1cm\times 1200cm \\
 & \Rightarrow \text{Volume=}\dfrac{22}{7}\times \dfrac{21}{10}cm\times \dfrac{21}{10}cm\times 1200cm \\
\end{align}\]
\[\Rightarrow \text{Volume=}22\times 3\times 21\times 12c{{m}^{3}}\] ……………………………(5)
We also know that, \[1000c{{m}^{3}}=1liter\] …………………………(6)
From equation (5) and equation (6), we get
Volume= \[\dfrac{22\times 3\times 21\times 12c{{m}^{3}}}{1000}liter=\dfrac{16632}{1000}liter=16.632liter\] .
Hence, the quantity of water that a pipe of length 12m and inner radius 2.1 cm is 16.632 liters.

Note: Here, the hidden information is that the pipe is in the shape of the cylinder. In this question, one can do a mistake by taking the length as 12 and radius as 2.1 in the formula \[\text{Volume=}\pi {{r}^{2}}l\] and write it as \[\text{Volume=}\dfrac{22}{7}\times 2.1\times 2.1\times 12\] . This is wrong. First, we need to convert the unit of length which is meter into centimeter, and then we can put it into the formula for further solution.