Question

) A hollow cylindrical copper pipe is 210 cm long. Its outer and inner diameters

are 10 cm and 6 cm respectively. Find the volume of copper used in making

the pipe and also find the area of rings.​

Answer 1

Solution :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){6}}\multiput(1,0)(2,0){2}{\line(0,1){6}}\multiput(0,0)(0,6){2}{\qbezier(0,0)(2,-0.6)(4,0)}\multiput(0,0)(0,6){2}{\qbezier(0,0)(2,0.6)(4,0)}\multiput(1,0)(0,6){2}{\qbezier(0,0)(1,-0.2)(2,0)}\multiput(1,0)(0,6){2}{\qbezier(0,0)(1,0.2)(2,0)}\multiput(2,0.07)(0,0.3){20}{\line(0,1){0.2}}\multiput(2,4)(0.3,0){7}{\line(1,0){0.2}}\multiput(2,2)(-0.27,0){4}{\line(-1,0){0.2}}\put(1.4,1.5){\bf\ 6 \: cm}\put(3.35,3.45){\bf 10 \: cm}\put(1.4,3){\bf 210 \: cm }\end{picture}$

Volume of Pipe :

> π r_1² h - π r_2² h

> π h ( r¹ + r² )( r¹ - r²)

> 22/7 × 210 × 16 × 4

> 22 × 30 × 16 × 4

> 42240 cm ².

Area Of Rings :

Area of Smaller Ring :

> 36 π cm ²

Area of Larger Ring :

> 100 π cm ² .

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Answer 2

Answer:

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Required Answer :-

Diagram

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){6}}\multiput(1,0)(2,0){2}{\line(0,1){6}}\multiput(0,0)(0,6){2}{\qbezier(0,0)(2,-0.6)(4,0)}\multiput(0,0)(0,6){2}{\qbezier(0,0)(2,0.6)(4,0)}\multiput(1,0)(0,6){2}{\qbezier(0,0)(1,-0.2)(2,0)}\multiput(1,0)(0,6){2}{\qbezier(0,0)(1,0.2)(2,0)}\multiput(2,0.07)(0,0.3){20}{\line(0,1){0.2}}\multiput(2,4)(0.3,0){7}{\line(1,0){0.2}}\multiput(2,2)(-0.27,0){4}{\line(-1,0){0.2}}\put(1.4,1.5){\bf\ 6 \: cm}\put(3.35,3.45){\bf 10 \: cm}\put(1.4,3){\bf 210 \: cm }\end{picture}$

Solution :-

Volume of pipe

= $\sf \pi {r_1}^2 h - \pi {r_2}^2 h$

= π h ( r¹ + r² )( r¹ - r²)

= 22/7 × 210 × 16 × 4

Cancelling 7 and 210

= 22 × 30 × 16 × 4

= 42240 cm ².

Area of rings

Area of Smaller Ring :-

36 π cm ²

Area of Larger Ring :-

100 π cm ²

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