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 1 $c{m^3}$ of wood has a mass of 0.6 gm.
Answer
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Hint: In this question first convert inner and outer diameter into radius then apply the formula of volume of cylindrical tube having inner and outer radius, later on multiply this volume by given mass, so use these concepts to reach the solution of the question.
Given data
Inner diameter (d) of cylindrical wood pipe is 24 cm.
Outer diameter (D) of cylindrical wood pipe is 28 cm.
The length (h) of the pipe is 35 cm.
1 $c{m^3}$ of wood has a mass of 0.6 gm.
So, inner radius (r) of the cylindrical wood pipe $ = \dfrac{{{\text{inner diameter}}}}{2} = \dfrac{d}{2} = \dfrac{{24}}{2} = 12$ cm.
So, outer radius (R) of the cylindrical wood pipe $ = \dfrac{{{\text{outer diameter}}}}{2} = \dfrac{D}{2} = \dfrac{{28}}{2} = 14$ cm.
Now we all know that the volume (V) of the cylindrical tube having inner and outer radius is given as
$ \Rightarrow V = \pi \left( {{R^2} - {r^2}} \right)h$.
Now, substitute the values in above equation we have
$V = \pi \left( {{{14}^2} - {{12}^2}} \right)35$
As we know that $\left[ {\pi = \dfrac{{22}}{7}} \right]$, so apply this in above equation we have
$V = \dfrac{{22}}{7}\left( {{{14}^2} - {{12}^2}} \right)35 = \left( {22 \times 5} \right)\left( {196 - 144} \right) = 110\left( {52} \right) = 5720{\text{ c}}{{\text{m}}^3}$
Now it is given that mass of 1 $c{m^3}$ wood = 0.6 gm.
Therefore mass of 5720 $c{m^3}$wooden pipe $ = 5720 \times 0.6 = 3432{\text{ gms}}$.
We can also convert this mass into kilograms (kg).
As we know $1{\text{ gm}} = \dfrac{1}{{1000}}{\text{ kg}}$, so divide by 1000 in 3432 gm we have,
Mass of wooden pipe $ = \dfrac{{3432}}{{1000}} = 3.342{\text{ kgs}}$.
So, this is the required answer.
Note: In such types of questions the key concept we have to remember is that always recall the formula of volume of cylindrical tube having inner and outer radius which is stated above, then first calculate inner and outer radius, then substitute these values in the formula and calculate the volume, than multiply this volume by given mass of 1 $c{m^3}$wood, we will get the required mass of the wood, we can also convert the mass of the wood into kilograms from grams by dividing by 1000 in the mass of the wood as above.
Given data
Inner diameter (d) of cylindrical wood pipe is 24 cm.
Outer diameter (D) of cylindrical wood pipe is 28 cm.
The length (h) of the pipe is 35 cm.
1 $c{m^3}$ of wood has a mass of 0.6 gm.
So, inner radius (r) of the cylindrical wood pipe $ = \dfrac{{{\text{inner diameter}}}}{2} = \dfrac{d}{2} = \dfrac{{24}}{2} = 12$ cm.
So, outer radius (R) of the cylindrical wood pipe $ = \dfrac{{{\text{outer diameter}}}}{2} = \dfrac{D}{2} = \dfrac{{28}}{2} = 14$ cm.
Now we all know that the volume (V) of the cylindrical tube having inner and outer radius is given as
$ \Rightarrow V = \pi \left( {{R^2} - {r^2}} \right)h$.
Now, substitute the values in above equation we have
$V = \pi \left( {{{14}^2} - {{12}^2}} \right)35$
As we know that $\left[ {\pi = \dfrac{{22}}{7}} \right]$, so apply this in above equation we have
$V = \dfrac{{22}}{7}\left( {{{14}^2} - {{12}^2}} \right)35 = \left( {22 \times 5} \right)\left( {196 - 144} \right) = 110\left( {52} \right) = 5720{\text{ c}}{{\text{m}}^3}$
Now it is given that mass of 1 $c{m^3}$ wood = 0.6 gm.
Therefore mass of 5720 $c{m^3}$wooden pipe $ = 5720 \times 0.6 = 3432{\text{ gms}}$.
We can also convert this mass into kilograms (kg).
As we know $1{\text{ gm}} = \dfrac{1}{{1000}}{\text{ kg}}$, so divide by 1000 in 3432 gm we have,
Mass of wooden pipe $ = \dfrac{{3432}}{{1000}} = 3.342{\text{ kgs}}$.
So, this is the required answer.
Note: In such types of questions the key concept we have to remember is that always recall the formula of volume of cylindrical tube having inner and outer radius which is stated above, then first calculate inner and outer radius, then substitute these values in the formula and calculate the volume, than multiply this volume by given mass of 1 $c{m^3}$wood, we will get the required mass of the wood, we can also convert the mass of the wood into kilograms from grams by dividing by 1000 in the mass of the wood as above.
Last updated date: 21st Sep 2023
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