Answer
Verified
426k+ 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
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What organs are located on the left side of your body class 11 biology CBSE
Write an application to the principal requesting five class 10 english CBSE
What is the type of food and mode of feeding of the class 11 biology CBSE
Name 10 Living and Non living things class 9 biology CBSE