Answer
Verified
419.4k+ views
Hint:First find the volumes of inner and outer cylinders separately by using the formula \[\pi {{r}^{2}}h\] and then use the formula, Total volume of wooden pipe = Volume of outer pipe – Volume of inner pipe to calculate the total volume of pipe. Then multiply the volume by 0.6 to get the total volume.
Complete step by step answer:
To find the mass of the cylinder we will first draw the diagram of the cylinder with given measures.
Now, we will write the given data with assuming the required notations,
Diameter of outer cylinder = D = 28 cm.
Therefore radius of outer cylinder $=R=\dfrac{D}{2}=\dfrac{28}{2}=14cm$ ………………………………….. (1)
Diameter of inner cylinder = d = 24 cm.
Therefore radius of inner cylinder $=r=\dfrac{d}{2}=\dfrac{24}{2}=12cm$ …………………………………………. (2)
Height of the cylinder = h =35 cm. ………………………………………………………………………………. (3)
Also, 1 $c{{m}^{3}}$ of wood has a mass of 0.6 g.
As we have given the mass per $c{{m}^{3}}$ of the wood therefore we will first find the total volume of the wooden cylinder so that we can easily calculate its total mass.
If we see the geometry of the figure then we can conclude that,
Total volume of wooden pipe = Volume of outer pipe – Volume of inner pipe ……………………… (4)
To find the total volume of wooden pipe we will first find out the inner and outer cylinder volumes. To find the individual volumes we should know the formula given below,
Formula:
Volume of cylinder = \[\pi {{r}^{2}}h\]
By using the formula given above we can write the formula for volume of outer cylinder as,
Volume of outer cylinder = \[\pi {{R}^{2}}h\]
If we put the value of equation (1) and equation (3) in the above equation we will get,
Volume of outer cylinder = \[\pi {{\left( 14 \right)}^{2}}\left( 35 \right)\] ……………………………………………………………………………… (5)
Also the formula for the volume of inner cylinder can be written as,
Volume of inner cylinder = \[\pi {{r}^{2}}h\]
If we put the values of equation (2) and equation (3) in the above equation we will get,
Volume of inner cylinder = \[\pi {{\left( 12 \right)}^{2}}\left( 35 \right)\] ………………………………………………………………………………. (6)
Now we will put the values of equation (5) and equation (6) in equation (4) to get the total volume of wooden pipe, Therefore,
Total volume of wooden pipe = \[\pi {{\left( 14 \right)}^{2}}\left( 35 \right)-\pi {{\left( 12 \right)}^{2}}\left( 35 \right)\]
Therefore, the total volume of wooden pipe = \[35\pi \left[ {{\left( 14 \right)}^{2}}-{{\left( 12 \right)}^{2}} \right]\]
Therefore, the total volume of wooden pipe = \[35\pi \left[ 196-144 \right]\]
Therefore, the total volume of wooden pipe = \[35\pi \left( 52 \right)\]
Therefore, total volume of wooden pipe = 5717.69 \[c{{m}^{3}}\]
Now as we have given in the problem,
1 $c{{m}^{3}}$ of wood has a mass of 0.6 g therefore,
5717.69 \[c{{m}^{3}}\] of wood have mass = \[5717.69\times 0.6\]
Therefore, the total mass of the wooden pipe = 3430.61 g.
Therefore, the total mass of wooden pipe = \[\dfrac{3430.61}{1000}\] Kg.
Therefore, the total mass of wooden pipe = 3.4306 Kg.
Therefore the total mass of the cylindrical wooden pipe is equal to 3.4306 Kg.
Note: You can directly use the formula \[Mass=Density\times \left( Volume\text{ }of\text{ }outer\text{ }pipe\text{ }\text{ }Volume\text{ }of\text{ }inner\text{ }pipe \right)\] as 0.6 is basically the density of the material and it will give you quick answer in competitive exams. Just be aware of silly mistakes while using this formula.
Complete step by step answer:
To find the mass of the cylinder we will first draw the diagram of the cylinder with given measures.
Now, we will write the given data with assuming the required notations,
Diameter of outer cylinder = D = 28 cm.
Therefore radius of outer cylinder $=R=\dfrac{D}{2}=\dfrac{28}{2}=14cm$ ………………………………….. (1)
Diameter of inner cylinder = d = 24 cm.
Therefore radius of inner cylinder $=r=\dfrac{d}{2}=\dfrac{24}{2}=12cm$ …………………………………………. (2)
Height of the cylinder = h =35 cm. ………………………………………………………………………………. (3)
Also, 1 $c{{m}^{3}}$ of wood has a mass of 0.6 g.
As we have given the mass per $c{{m}^{3}}$ of the wood therefore we will first find the total volume of the wooden cylinder so that we can easily calculate its total mass.
If we see the geometry of the figure then we can conclude that,
Total volume of wooden pipe = Volume of outer pipe – Volume of inner pipe ……………………… (4)
To find the total volume of wooden pipe we will first find out the inner and outer cylinder volumes. To find the individual volumes we should know the formula given below,
Formula:
Volume of cylinder = \[\pi {{r}^{2}}h\]
By using the formula given above we can write the formula for volume of outer cylinder as,
Volume of outer cylinder = \[\pi {{R}^{2}}h\]
If we put the value of equation (1) and equation (3) in the above equation we will get,
Volume of outer cylinder = \[\pi {{\left( 14 \right)}^{2}}\left( 35 \right)\] ……………………………………………………………………………… (5)
Also the formula for the volume of inner cylinder can be written as,
Volume of inner cylinder = \[\pi {{r}^{2}}h\]
If we put the values of equation (2) and equation (3) in the above equation we will get,
Volume of inner cylinder = \[\pi {{\left( 12 \right)}^{2}}\left( 35 \right)\] ………………………………………………………………………………. (6)
Now we will put the values of equation (5) and equation (6) in equation (4) to get the total volume of wooden pipe, Therefore,
Total volume of wooden pipe = \[\pi {{\left( 14 \right)}^{2}}\left( 35 \right)-\pi {{\left( 12 \right)}^{2}}\left( 35 \right)\]
Therefore, the total volume of wooden pipe = \[35\pi \left[ {{\left( 14 \right)}^{2}}-{{\left( 12 \right)}^{2}} \right]\]
Therefore, the total volume of wooden pipe = \[35\pi \left[ 196-144 \right]\]
Therefore, the total volume of wooden pipe = \[35\pi \left( 52 \right)\]
Therefore, total volume of wooden pipe = 5717.69 \[c{{m}^{3}}\]
Now as we have given in the problem,
1 $c{{m}^{3}}$ of wood has a mass of 0.6 g therefore,
5717.69 \[c{{m}^{3}}\] of wood have mass = \[5717.69\times 0.6\]
Therefore, the total mass of the wooden pipe = 3430.61 g.
Therefore, the total mass of wooden pipe = \[\dfrac{3430.61}{1000}\] Kg.
Therefore, the total mass of wooden pipe = 3.4306 Kg.
Therefore the total mass of the cylindrical wooden pipe is equal to 3.4306 Kg.
Note: You can directly use the formula \[Mass=Density\times \left( Volume\text{ }of\text{ }outer\text{ }pipe\text{ }\text{ }Volume\text{ }of\text{ }inner\text{ }pipe \right)\] as 0.6 is basically the density of the material and it will give you quick answer in competitive exams. Just be aware of silly mistakes while using this formula.
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
State the differences between manure and fertilize class 8 biology CBSE
Why are xylem and phloem called complex tissues aBoth class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
What would happen if plasma membrane ruptures or breaks class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What precautions do you take while observing the nucleus class 11 biology CBSE
What would happen to the life of a cell if there was class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE