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.
Last updated date: 22nd Mar 2023
•
Total views: 306.9k
•
Views today: 5.85k
Answer
306.9k+ views
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.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
