Question

# A metal pipe is $$77$$ cm long. The inner diameter of a cross section is $$4$$ cm, the outer diameter being $$4.4$$ cm (see figure). Find its(i) inner curved surface area.(ii) outer curved surface area(iii) Total surface area

Solution

## Given:$$\Rightarrow$$Inner radius $$=\cfrac{4}{2}=2$$ cm $$={r}_{1}$$$$\Rightarrow$$Outer radius $$=\cfrac{4.4}{2}=2.2$$cm $$={r}_{2}$$$$\Rightarrow$$Height $$=77$$ cmSolution:(i) Curved S.A$$=2\pi {r}_{1}h$$ (inner)$$=2\times \cfrac{22}{7}\times 2\times 77=968$$ cm$$^{2}$$(ii) Curved S.A (outer)$$=2\pi {r}_{2}h$$$$=2\times \cfrac{22}{7}\times 2.2\times 77{cm}^{2}=(22\times 22\times 2.2)$$ cm$$^{2}$$$$=1064.8{cm}^{2}$$(iii) Total S.A of pipe $$=$$ CSA of inner surface $$+$$ CSA of outer surface $$+$$ Area of circural base and top$$=968+1064.8+2\pi ({(2.2)}^{2}-2\pi {(2)}^{2})$$$$=2032.8+5.28$$ cm$$^{2}$$$$=2038.08$$ cm$$^{2}$$MathematicsRS AgarwalStandard IX

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