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 find it's
(I) Inner curved surface area.
(ii) Outer curved surface area.
(iii) Total surface area.​

Answer 1

${\bold{\pink{\underline{\red{So}\purple{lut}\green{ion}\orange{:-}}}}}$

$\bf\boxed\star\pink{\underline{\underline{{(i)\:Inner\: Curved\: Surface\:area}}}}$

$\bf\:Given,$

$\bf\: Diameter=4\:cm$

$\bf\:radius=\dfrac{Diameter}{2}$

$\bf\:radius=\dfrac{4}{2}=2\:cm$

$\bf\: height=77\:cm$

$\bf\:Inner\:C.\:S.\:A=2\pi{rh}$

$\bf\:Inner\:C.\:S.\:A=2\times\dfrac{22}{7}\times\:2\times\:77\:c{m}^{2}$

$\bf\:Inner\:C.\:S.\:A=2\times\:22\times\:2\times\:11\:c{m}^{2}$

$\bf\:Inner\:C.\:S.\:A=968\:c{m}^{2}$

$\bf\boxed\star\orange{\underline{\underline{{(ii)\:Outer\: Curved\: Surface\:area}}}}$

$\bf\:Given,$

$\bf\: Diameter=4.4\:cm$

$\bf\:radius=\dfrac{Diameter}{2}$

$\bf\:radius=\dfrac{4.4}{2}=2.2\:cm$

$\bf\: height=77\:cm$

$\bf\:Outer\:C.\:S.\:A=2\pi{rh}$

$\bf\:Outer\:C.\:S.\:A=2\times\dfrac{22}{7}\times\:2.2\times\:77\:c{m}^{2}$

$\bf\:Outer\:C.\:S.\:A=2\times\:22\times\:2.2\times\:11\:c{m}^{2}$

$\bf\:Outer\:C.\:S.\:A=1064.80\:c{m}^{2}$

$\bf\boxed\star\blue{\underline{\underline{{(iii)\:Total\: Surface\:area}}}}$

$\bf\: Given,$

$\bf\:R=2.2\:cm$

$\bf\:r=2\:cm$

$\bf\:h=77\:cm$

$\bf\:Area\:of\:upper\:ring=\pi({R}^{2}-{r}^{2})$

$\bf\: Area\:of\:upper\:ring=\dfrac{22}{7}\times\:{(2.2)}^{2}-{(2)}^{2}\:c{m}^{2}$

$\bf\: Area\:of\:upper\:ring=\dfrac{22}{7}\times\:4.84-4\:c{m}^{2}$

$\bf\: Area\:of\:upper\:ring=22\times\:0.12\:c{m}^{2}$

$\bf\: Area\:of\:upper\:ring=2.64\:c{m}^{2}$

$\bf\: Area\:of\:lower\:ring=2.64\:c{m}^{2}$

$\bf\:T.S.A=Inner\:C.S.A+Outer\:C.S.A+Area\:of\:lower\:ring+Area\:of\:upper\:ring$

$\bf\:T.S.A= 968+1064.80+2.64+2.64$

$\bf\:T.S.A=2038.08\:c{m}^{2}$

Answer 2

i) Inner curved surface area

Given :

• Height (h) = 77 cm
• Diameter 1 = 4 cm

When we convert it in radius 1 :-

→ r = d ÷ 2

→ r = 4 cm ÷ 2 = 2 cm

• Diameter 2 = 4.4 cm

Again we will concert it in radius 2 :-

→ r= d ÷ 2

→ r = 4.4 cm ÷ 2 = 2.2 cm

According to the question,

Inner curved surface area = $\sf{2 \pi rh}$

$\rightarrow \sf{2 \times \frac{22}{7} \times 2 \times 77 } \\ \rightarrow \sf \red{368 \: {cm}^{2} }$

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ii)Outer curved surface area

Given :

• Height = 77 cm
• Radius 2 = 2.2 cm

According to the question,

Outer curved surface area = $\sf{2 \pi rh}$

$\rightarrow \sf{2 \times \frac{22}{7} \times 2.2\times 77 } \\ \rightarrow \sf \red{1064.8 \: {cm}^{2} }$

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iii) Total surface area

Total surface area of pipe = CSA of inner surface area + CSA of outer surface area + Area of both circular ends of pipe

$\rightarrow \sf{2 \pi r _{1} h} + {2 \pi r _{2} h} + 2 \pi ( {{r} \: ^{2}_{2} +{r} \: ^{2}_{1 }}) \\ \rightarrow \sf{968 + 1064.8 + 2 \pi ( {2.2)}^{2} + {(2)}^{2} } \\ \rightarrow \sf{(2032.8 + 2 \times \frac{22}{7} \times 0.84) } {cm}^{2} \\ \rightarrow \sf{(2032.8 + 5.28) {cm}^{2} } \\ \therefore \sf \red{2038.08 { \: cm}^{2} }$