Question

The volume of a metallic cylindrical pipe is 748 cm. Its length is 14 cm and its external radius is 9 cm. Find its thickness.​

Answer 1

$\huge\textbf{Question:-}$

Q.The volume of a metallic cylindrical pipe is 748 cm. Its length is 14 cm and its external radius is 9 cm. Find its thickness.

$\textbf{Answer:-}$

GIVEN

• The volume of a metallic cylindrical pipe is 748 cm³
• length is 14 cm
• radius is 9 cm

REQUIRED TO FIND

• Find its thickness.

SOLUTION

volume of cylinder = volume of metal used

• π ( R² - r² ) h = 748cm³

$\frac{22}{ \cancel7} ( {9}^{2} - {r}^{2} ) \cancel14 \: = 748 \\ 81 - {r}^{2} = \frac{748}{22 \times 2} \\ 81 - {r}^{2} = 17 \\ 81 - 17 = {r}^{2} \\ {r }^{2} = 64 \\ r = \sqrt{64 } \\ r = 8$

so, r = 8

Thickness of pipe = R - r

• 9 - 8 = 1

Therefore the thickness of metal pipe is 1cm

:) !!

Answer 2

Answer:

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){6}}\multiput(1,0)(2,0){2}{\line(0,1){6}}\multiput(0,0)(0,6){2}{\qbezier(0,0)(2,-0.6)(4,0)}\multiput(0,0)(0,6){2}{\qbezier(0,0)(2,0.6)(4,0)}\multiput(1,0)(0,6){2}{\qbezier(0,0)(1,-0.2)(2,0)}\multiput(1,0)(0,6){2}{\qbezier(0,0)(1,0.2)(2,0)}\multiput(2,0.07)(0,0.3){20}{\line(0,1){0.2}}\multiput(2,4)(0.3,0){7}{\line(1,0){0.2}}\multiput(2,2)(-0.27,0){4}{\line(-1,0){0.2}}\put(1.4,1.5){\bf{8\ cm}}\put(3.35,3.45){\bf{9\ cm}}\put(1.4,3){\bf{14\ cm}}\end{picture}$

Given :

★ The volume of a metallic cylindrical pipe is 748 cm.

★ Length of metallic cylindrical pipe is 14 cm.

★ External radius of cylindrical pipe is 9 cm.

To Find :

★ Internal radius of cylindrical pipe is 8 cm.

★ Thickness of cylindrical pipe.

Using Formulas :

★ Volume of cylinder = πR²h  - πr²h

★ Thickness = External radius - Internal radius

Solution :

Here we have given that volume of cylindrical pipe is 747 cm, lenght of cylindrical pipe is 14 cm and external radius is 9 cm. So, finding the Internal radius.

${\implies{Volume\:of\:cylinder = \pi{R}^{2}h -\pi{r}^{2} h}}$

Substituting all all the values in the formual.

• $\bull$ Volume of Cylinder = 748
• $\bull$ External radius = 9 cm
• $\bull$ Height of radius = 14 cm

$\begin{gathered}\implies{748=\bigg(\dfrac{22}{7} \times {(9)}^{2}\times 14\bigg) - \bigg(\dfrac{22}{7} \times {(r)}^{2} \times 14\big)}\\\\\implies{748 = \bigg(\dfrac{22}{\cancel{7}} \times (9 \times 9) \times \cancel{14}\bigg) -   \bigg(\dfrac{22}{\cancel{7}} \times {(r)}^{2} \times {\cancel{14}} \bigg)} \\  \\ \implies{748 = \bigg(22 \times 9 \times 9\times 2\bigg) - \bigg(22 \times (r)^2 \times 2\bigg)} \\  \\ \implies{748 =44 \times 81- 44r^2}\\\\\implies{748 =44(81- r^2)}\\\\\implies{(81- r^2) =  \dfrac{748}{44}}\\\\\implies{(81- {r}^{2}) = \cancel{\dfrac{748}{44}}}\\\\\implies{(81- r^2) =  17}\\\\\implies{r^2 = - 17 + 84}\\\\\implies{r^2= 64}\\\\\implies{r= \sqrt{64}}\\\\\implies{r= 8 \: cm} \end{gathered}$

Hence, the Internal radius is 8 cm.

$\rule{190}{1}$

Now, we know the External radius and Internal radius. So finding the thickness of metallic cylindrical pipe :

$\begin{gathered} \quad\Rightarrow{Thickness = External_{(radius)} - Internal_{(radius)}} \\ \\ \quad\Rightarrow{Thickness = 9 - 8} \\ \\ \quad\Rightarrow{Thickness = 1 \: cm} \end{gathered}$

Hence, the thickness is 1 cm.

$\rule{190}{1}$

#Learn More :

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

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