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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 4.4 cm. Find itsi) inner curved surface areaii) outer curved surface areaiii) total surface area.

Given :
Inner radius (r) of cylindrical pipe = $$\frac{4}{2}$$ cm = 2 cm
outer radius (R) of cylindrical pipe = $$\frac{4.4}{2}$$ cm = 2.2 cm
Height (h) Of cylindrical pipe = Length Of cylindrical pipe = 77 cm

i) CSA of inner surface of pipe
= $$2{\pi}rh$$
= $$2 × \frac{22}{7} × 2 × 77$$ $${cm}^2$$
= $$2 × 22 × 2 × 11$$ $${cm}^2$$
= 968 $${cm}^2$$

ii) CSA of inner surface of pipe
= $$2{\pi}{R}h$$
= $$2 × \frac{22}{7} × 2.2 × 77$$
= $$2 × 22 × 2.2$$ $${cm}^2$$
= 1064.8 $${cm}^2$$

iii) Total surface area of pipe
= CSA of inner surface + CSA of outer surface + Area of both circular ends of pipe
= $$2{\pi}{r}h$$ + $$2{\pi}{R}h$$ + $$2{\pi} [(R)^2 - (r)^2]$$
= $$[968 + 1064.8 + 2{\pi}{(2.2)^2 - (2)^2}] {cm}^2$$
= $$2032.8 + 2 × \frac{22}{7} × 0.84$$ $${cm}^2$$
= (2032.8 + 5.28) $${cm}^2$$
= 2038.08 $${cm}^2$$

Therefore, the total surface area of the cylindrical pipe is 2038.08 $${cm}^2$$.