Question

The given figure shows a metal pipe $$77cm$$ long. The inner diameter of cross section is $$4cm$$ and the outer one is $$4.4cm$$.
Find its
(i) inner curved surface area
(ii) outer curved surface are
(iii) total surface area

Answer 1

Given

Length of metal pipe $$(h)=77cm$$

Inner diameter $$=4cm$$

Outer diameter $$=4.4cm$$

So, inner radius $$(r)=\dfrac42=2cm$$

And outer radius $$(R)=2.2cm$$

(i) Inner curved surface area $$=2\pi rh=2\times \dfrac{22}7\times 2\times 77{ cm }^{ 2 }=968{ cm }^{ 2 }\quad $$

(ii) Outer surface area $$=2\pi Rh=2\times \dfrac{22}7\times 2.2\times 77=1064.8{ cm }^{ 2 }$$

(iii) Surface area of upper and lower rings $$=2\left[ \pi { R }^{ 2 }-\pi { r }^{ 2 } \right] =2\times \dfrac{22}7[{ (2.2) }^{ 2 }-{ 2 }^{ 2 }] \ { cm }^{ 2 }=5.28{ cm }^{ 2 }$$

Hence, Total surface area $$=(968+1064.8+5.28){cm}^{2}=2038.08{cm}^{2}$$