Question

$\huge{\textbf{\tests{{\color{navy}{Question}}{\purple{ut}}{\pink}{ion❧}}}}$

A cylinder tube open at both ends is made of metal. The internal diameter of the tube is 7.2 cm and its length is 12 cm the metal thickness is 0.4 m. Calculate the volume of the metal.

Please solve this.​

Answer 1

$\large\underline{\sf{\red{Given}}}$

✭ The internal diameter of tube = 7.2 cm

✭ Length of tube = 12 cm

✭ Thickness of metal = 0.4 m = 40 cm

$\large\underline{\sf{\blue{Diagram}}}$

$\quad\qquad\:\:$ $\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){6}}\multiput(1,0)(2,0){2}{\line(0,1){6}}\multiput(0,0)(0,6){2}{\qbezier(0,0)(2,-0.6)(4,0)}\multiput(0,0)(0,6){2}{\qbezier(0,0)(2,0.6)(4,0)}\multiput(1,0)(0,6){2}{\qbezier(0,0)(1,-0.2)(2,0)}\multiput(1,0)(0,6){2}{\qbezier(0,0)(1,0.2)(2,0)}\multiput(2,0.07)(0,0.3){20}{\line(0,1){0.2}}\multiput(2,4)(0.3,0){7}{\line(1,0){0.2}}\multiput(2,2)(-0.27,0){4}{\line(-1,0){0.2}}\put(1.4,1.5){\bf\large 3.6\:cm}\put(3.35,3.45){\bf 43.6\:cm}\put(1.4,3){\bf 12\:cm}\end{picture}$

$\large\underline{\sf{\purple{Note}}}$

✭ If you are not able to see the diagram, please refer the attachment

$\large\underline{\sf{\orange{To\:Find}}}$

✭ Volume of the metal?

$\large\underline{\sf{\green{Solution}}}$

Things to know before solving this question,

◈ $\underline{\boxed{\sf{Volume_{(cylinder)} = \pi r^2 h}}}$

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Calculating the volume of tube,

➝ $\small\sf Volume_{(tube)} = \pi r^2 h$

We have,

• Radius = d/2 = 7.2/2 = 3.6 cm

• Height = length = 12 cm

• π = 22/7

Putting all values,

➝ $\small\sf Volume_{(tube)} = \dfrac{22}{7} \:\times\:(3.6)^2 \:\times\:12$

➝ $\small\sf Volume_{(tube)} = \dfrac{22}{7} \:\times\:12.96 \:\times\:12$

➝ $\small\sf Volume_{(tube)} = \dfrac{22\:\times\:12.96 \:\times\:12}{7}$

➝ $\small\sf Volume_{(tube)} = \dfrac{3421.44}{7}$

➝ $\small\sf Volume_{(tube)} = {\cancel{\dfrac{3421.44}{7}}}\:(Cancelling)$

➝ $\small\sf \pink{Volume_{(tube)} \:\approx\: 488.7\:cm^3}\:\dashrightarrow\:(1)$

Calculating volume of tube including volume of metal,

➳ $\small\sf Volume_{(tube, \:metal)} = \pi r^2 h$

We have,

• Radius = internal radius + thickness = 3.6 + 40 = 43.6 cm

• Height = length = 12 cm

• π = 22/7

Putting all values,

➳ $\small\sf Volume_{(tube, \:metal)} = \dfrac{22}{7}\:\times\:(43.6)^2 \:\times\:12$

➳ $\small\sf Volume_{(tube, \:metal)} = \dfrac{22}{7}\:\times\:1900.96 \:\times\:12$

➳ $\small\sf Volume_{(tube, \:metal)} = \dfrac{22\:\times\:1900.96 \:\times\:12}{7}$

➳ $\small\sf Volume_{(tube, \:metal)} = \dfrac{501853.44}{7}$

➳ $\small\sf Volume_{(tube,\: metal)} = {\cancel{\dfrac{501853.44}{7}}}\:(Cancelling)$

➳ $\small\sf \pink{Volume_{(tube, \:metal)}\:\approx\: 71693.5\:cm^3}\:\dashrightarrow\:(2)$

Calculating volume of metal,

⪼ $\small\sf Volume_{(metal)} = (2) - (1)$

We have,

• (1) = 488.7 cm³

• (2) = 71693.5 cm³

Putting all values,

⪼ $\small\sf Volume_{(metal)} = 71693.5 - 488.7$

⪼ $\small\sf \pink{Volume_{(metal)} \:\approx\: 71204.8\:cm^3}$

$\therefore\:{\underline{\sf{Volume\:of\:metal\:\approx\:\bf{71,205\:cm^3}}}}$

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Answer 2

Solution :

• The internal diameter of the tube is 7.2 cm and it's length is 12 cm.

• The thickness of the metal is 0.4 m or 40 cm

We have to calculate the volume of the metal .

Volume of metal = External Volume - Internal Volume

> π r_1² h - π r_2² h

> πh( r_1² - r_2²)

> πh( 43.6 + 3.6)( 43.6 - 3.6). [ r_1 = 40+ 3.6 and r_2 = 3.6 ]

> 22/7 × 12 × 47.2 × 40

> 71205 cm³ approximately .

Answer : The volume of the metal is 71205 cm³ approximately .

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Additional Information :

$\boxed{\begin{minipage}{6.2 cm}\bigstar \:\underline{\textbf{Formulae Related to Cylinder :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:Area\:of\:Base\:and\:top =\pi r^2 \\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:Curved \: Surface \: Area =2 \pi rh\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:Total \: Surface \: Area = 2 \pi r(h + r)\\ \\{\textcircled{\footnotesize\textsf{4}}} \: \:Volume=\pi r^2h\end{minipage}}$

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