Question

How much metal is required to make a 20 metre long pipe, if its inner and outer diameter are 6 metre and 8 metre respectively.

Answer 1

$\underline {\pink{ Dimensions \: of \: a \: metal \:pipe : }}$

$Length \:of \:the \: pipe (h) = 20 \:m$

$Inner \: Diameter (d) = 6 \:m$

$Inner \: radius (r) = \frac{d}{2}$

$= \frac{6}{2}$

$= 3 \: m$

$Outer \: Diameter (D) = 8\:m$

$Outer \: radius (R) = \frac{D}{2}$

$= \frac{8}{2}$

$= 4 \: m$

$\red{ Metal \: required \: to \: make \:the \:pipe }$

$= \pi h ( R^{2} - r^{2} )$

$= \pi h ( R + r )( R - r )$

$= \frac{22}{7} \times 20 \times ( 4 + 3 )( 4 - 3 )$

$= \frac{22}{7} \times 20 \times 7 \times 1$

$= 22\times 20$

$= 440 \: m^{3}$

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