Question

The inner diameter of a cylindrical wooden pipe is $ 24 $ cm and its outer diameter is $ 28 $ cm. The length of the pipe is $ 35 $ cm. Find the mass of the pipe, if $ 1c{m^3} $ of wood has a mass of $ 0.6g $ .

Answer 1

Hint: The given question deals with the concepts of mensuration. Menstruation involves the study of area, perimeter and volume of shapes and solid figures such as cuboid, cylinder, etc. The formulae for volume of cylinder should be learnt for solving the given question. One should also be thorough with the working of unitary methods for dealing with such types of questions.

Complete step-by-step answer:
In the given question, we are required to find the mass of the pipe. The dimensions as well as the density of the cylindrical hollow pipe is provided to us in the question itself.
So, we first have to find the volume of material wood used in making the pipe. Then, we can determine the mass of the pipe using the density of wood given to us.
So, Volume of the pipe can be calculated by subtracting the inner cylinder volume from the outer cylinder volume.

So, Volume of pipe $ = \pi {R^2}h - \pi {r^2}h $ , where r is the inner radius and R is the outer radius.
  $ \Rightarrow $ $ \pi h\left( {{R^2} - {r^2}} \right) $
 $ \Rightarrow $ $ \left( {\dfrac{{22}}{7}} \right)\left( {35cm} \right)\left( {{{\left( {28cm} \right)}^2} - {{\left( {24cm} \right)}^2}} \right) $
 $ \Rightarrow $ $ \left( {\dfrac{{22}}{7}} \right)\left( {35cm} \right)\left( {{{\left( {28cm} \right)}^2} - {{\left( {24cm} \right)}^2}} \right) $
 $ \Rightarrow $ $ \left( {22} \right)\left( 5 \right)\left( {784 - 576} \right)c{m^3} $
 $ \Rightarrow $ $ 110\left( {208} \right)c{m^3} $
 $ \Rightarrow $ \[22880c{m^3}\]
Therefore, the volume of pipe is \[22880c{m^3}\] .
Now, the mass of wood can be calculated using the density related information given to us.
 $ 1c{m^3} $ of wood has a mass of $ 0.6g $
So, \[22880c{m^3}\] of wood would have a mass of $ 22880 \times 0.6g $
Therefore, \[22880c{m^3}\] of wood would have a mass of $ 13728g $ .
 \[22880c{m^3}\] of wood would have a mass of $ 13.728kg $
So, the correct answer is “ $ 13.728kg $ ”.

Note: Care should be taken while doing calculations. Unitary methods should be used carefully. Unit conversion should also be carried out with utmost care as it can be a cumbersome process. Always, report your final answers in SI units to avoid mistakes.