# Q : 3    A metal pipe is $\small 77\hspace{1mm}cm$ long. The inner diameter of a cross section is 4 cm, the outer diameter being $\small 4.4 \hspace{1mm}cm$ (see Fig. $\small 13.11$). Find its          (iii) total surface area.

Note: There are two surfaces, inner and outer.

Given,

Height of the cylinder, $h = 77\ cm$

Outer diameter  = $r_1 = 4.4\ cm$

Inner diameter  = $r_2 = 4\ cm$

Outer curved surface area = $2\pi r_1h$

Inner curved surface area = $2\pi r_2h$

Area of the circular rings on top and bottom = $2\pi(r_2^2-r_1^2)$

$\therefore$ The total surface area of the pipe = $2\pi r_1h +2\pi r_2h+ 2\pi(r_2^2-r_1^2)$

$\\ = [968 + 1064.8 + 2\pi {(2.2)^2 - (2)^2}]\\ \\ = (2032.8 + 2\times \frac{22}{7}\times 0.84) \\ \\ = (2032.8 + 5.28) \\ = 2038.08\ cm^2$

Therefore, the total surface area of the cylindrical pipe is $2038.08\ cm^2$

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