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A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4 point 4 cm. Find its (iii) total surface area.

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.

          

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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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