Question

The external radius of a 14-cm-long metallic pipe is 9cm, and the pipe is 1cm thick. Find the volume of the metal used in the pipe. If the mass of 1cm³ metal is 8.5 g, find the mass of the pipe.

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Answer 1

$\sf\bf\underline{\underline{Question : }}$

The external radius of a 14-cm-long metallic pipe is 9cm, and the pipe is 1cm thick. Find the volume of the metal used in the pipe. If the mass of 1cm³ metal is 8.5 g, find the mass of the pipe.

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$\sf\bf\underline{\underline{Given : }}$

• Length of the metallic pipe = 14 cm
• Thickness of the pipe = 1 cm
• External radius of the metallic pipe = 9 cm
• Mass of 1cm³ metal = 8.5 g

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$\sf\bf\underline{\underline{To \: Find : }}$

• Volume of the metal used in the pipe = ?
• Mass of the pipe = ?

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$\sf\bf\underline{\underline{Solution : }}$

~ Formula Used :

• Volume of the metal :

$\sf \pink{ \: \: \: \: \: ⇢} \: \: \: \: \: \small{\color{green}{\fbox{\textsf{\textbf{ V = πh(R² - r²)}}}}}$

Where :

• ➻ V = Volume
• ➻ π = 22/7
• ➻ h = Height
• ➻ R is the radius of the outer surface
• ➻ r is the radius of the inner surface

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~ Finding the Internal Radius :

$\sf \red{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⟼} \: \: \: \: \: \: \: \small{\color{blue}{\fbox{\textsf{\textbf{ Internal Radius (r) = External Radius (R) - Thickness}}}}}$

$\sf{{ \: \: \: \: \: \: \: \: \: \: \: \red{⟼} \: \: \: \: \: \bf (9 - 1) cm\: }{ \: }}$

$\sf{{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \red{⟼} \: \: \: \: \: \: \: \: \: \: \: \bf 8 cm\: }{ \: }}$

$\bf \pink{Hence, The \: internal \: radius \: of \: the \: pipe = \green{8 cm.}}$

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~ Calculating the Volume of the Metal :

$\sf { \: \: \: \: \: \: \: \: \: \: \: ⟼} \: \: \: \: \: \: \: \: \: \: \: \small{{\fbox{\textsf{\textbf{ V = πh(R² - r²)}}}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{⟼ }\: \: \: \: \: \: \: \bf{ \frac{22}{7} \times 14( {9}^{2} - {8}^{2}) {cm}^{3} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{⟼} \: \: \: \: \: \: \: \: \: \bf{44(81 - 64) {cm}^{3} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{⟼} \: \: \: \: \: \: \: \: \: \: \: \: \bf{44 \times 17 {cm}^{3} }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{⟼} \: \: \: \: \: \: \: \: \: \: \: \: \: \bf{748 {cm}^{3} }$

$\bf\green{Hence, the \: volume \: of \: the \: metal \: used \: in \: the \: pipe \: = \pink{ 748 cm³}}$

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~ Calculating the Mass of the Pipe :

$\sf{ \: \: \: \: \: \: \: \: ↠ } \: \: \: \: \: \sf \bold{Total \: mass \: of \: the \: pipe = Mass \: of \: 1 cm³ \: metal × Volume \: of \: the \: metal. }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{↠} \: \: \: \: \: \: \: \bf{8.5 \times 748g}$

$\sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ↠ \: \: \: \: \: \: \: \: \: \: } \bf{6358g }$

$\sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ↠ \: \: \: \: \: \: \: \: \: \: } \bf{ 6.358kg}$

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~ Final Answer :

• ➻ The volume of the metal used in the pipe is 748 cm³.
• ➻ The Mass of the metallic pipe is 6.358 kg.

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Answer 2

Explanation:

Given

• The external radius of a 14-cm-long metallic pipe is 9cm, and the pipe is 1cm thick. Find the volume of the metal used in the pipe. If the mass of 1cm³ metal is 8.5 g, find the mass of the pipe

To Find

• Mass Of Pipe?

Solution

• ↪The volume of the metal used in the pipe is 748 cm³.

• ↪The Mass of the metallic pipe is 6.358 kg.

For Solution See Attachment!

I hope you satisfied by my Answer✔︎