The external diameter of a cylindrical shaped iron pipe is $24 c m$ and its length is $20 c m$ . If the thickness of the pipe is $1 c m$ , find the total surface area of the pipe(in $c m^{2}$ ).

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Solution

We have,
Height of pipe $(h) = 20 c m$

External diameter $= 25 c m$

External radius $(R) = 25 / 2 = 12.5 c m$

Internal diameter $= 25 - (1 + 1) = 23 c m$

Internal radius $(r) = 23 / 2 = 11.5 c m$

Total surface area
$= 2 π (R + r) (R - r + h)$

$= 2 π (12.5 + 11.5) (12.5 - 11.5 + 20)$

$= 2 π (24) (21)$

$= 1008 π c m^{2}$

$= 3168 c m^{2}$

Hence, the total surface area of the cylinder $= 3168 c m^{2}$ .

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