Question

1.5 km of thin cylindrical wire of diameter 1.6mm can be made by melting the material of a hollow metallic pipe
of length 24cm and thickness 4cm . Find the internal diameter of the pipe .

Answer 1

$\begin{array}{|c|c|}\cline{1-2}\textbf{Cylindrical wire}&\textbf{Metallic pipe}\\\cline{1-2}\text{Length( h_1 )=1.5 km=150000 cm}&\text{Length( h )=24 cm}\\\text{Radius( r_1 )=0.8 mm= 0.08 cm}&\text{External radius ( R )}\\&\text{Internal radius ( r ) (To be found)}\\&\text{Width, \;\;R-r = 4 cm}\\\cline{1-2}\end{array}$

$\text{As per given data,}$

$\textbf{Volume of cylindrical wire}=\textbf{Volume of metalic pipe}$

$\implies\,\bf\pi\,{r_1}^2\,h_1=\bf\pi\,h(R^2-r^2)$

$\implies\,{r_1}^2\,h_1=h(R+r)(R-r)$

$\implies\,(0.08)^2(150000)=24(R+r)(4)$

$\implies\,(0.0064)(150000)=24(R+r)(4)$

$\implies\,(64)(15)=24(R+r)(4)$

$\implies\,(16)(15)=24(R+r)$

$\implies\,(2)(15)=3(R+r)$

$\implies\,(2)(5)=(R+r)$

$\implies\bf\,R+r=10\;$......(1)

$\text{Also,}\bf\;R-r=4\;$.......(2)

$\text{Adding (1) and (2), we get}$

$2\,R=14$

$R=7\;\text{cm}$

$\text{Put R=7 in (1), we get}$

$7+r=10$

$r=3\;\text{cm}$

$\therefore\textbf{Internal radius is 3 cm}$

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A. 1 :

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