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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
464131_6abba180a0f44d089f2ea1d22fc28271.png


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 $$=77$$ cm

Solution:
(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$$^{2}$$

Mathematics
RS Agarwal
Standard IX

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