Question

3.
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 Fig. 13.11). Find its
(i) inner curved surface area,
(ii) outer curved surface area,
(iii) total surface area.​

Answer 1

Given :-

Length of pipe = > 77 cm

Inner Diameter = > 4 cm

Outer Diameter = > 4.4 cm

To Find :-

(i) inner curved surface area,

(ii) outer curved surface area,

(iii) total surface area.

Solution :-

(i) Inner curved surface area,

Radius of Inner C.S.A = > 2 cm

$Inner \: C.S.A \: \: of \: Pipe = > 2\pi \: rh \\ \\ Inner \: C.S.A \: \: of \: Pipe = > \: 2 \times \frac{22}{7} \times 2 \times 77 \\ \\ Inner \: C.S.A \: \: of \: Pipe = >2 \times \frac{22}{\cancel {7}} \times 2 \times \cancel {77} \\ \\ Inner \: C.S.A \: \: of \: Pipe = >2 \times 22 \times 2 \times 11\\ \\ Inner \: C.S.A \: \: of \: Pipe = >968 \: {cm}^{2}$

(ii) Outer curved surface area

Radius of Inner C.S.A = > 2.2 cm

$Outer \:\: C.S.A \: \: of \: Pipe = > 2\pi \: rh \\ \\ Outer \: C.S.A \: \: of \: Pipe = > \: 2 \times \frac{22}{7} \times 2.2 \times 77 \\ \\ Outer \: C.S.A \: \: of \: Pipe = >2 \times \frac{22}{\cancel {7}} \times 2.2 \times \cancel {77} \\ \\ Outer \: C.S.A \: \: of \: Pipe = >2 \times 22 \times 2.2 \times 11 \\ \\ Outer \: C.S.A \: \: of \: Pipe = >1064.8 \: {cm}^{2} </strong></p><p><strong>[tex] Outer \:\: C.S.A \: \: of \: Pipe = > 2\pi \: rh \\ \\ Outer \: C.S.A \: \: of \: Pipe = > \: 2 \times \frac{22}{7} \times 2.2 \times 77 \\ \\ Outer \: C.S.A \: \: of \: Pipe = >2 \times \frac{22}{\cancel {7}} \times 2.2 \times \cancel {77} \\ \\ Outer \: C.S.A \: \: of \: Pipe = >2 \times 22 \times 2.2 \times 11 \\ \\ Outer \: C.S.A \: \: of \: Pipe = >1064.8 \: {cm}^{2}$

(iii) Total surface area.

$= > Inner \: C.S.A + Outer \: C.S.A + 2 \times Area \: of \: Circles \\ \\ = > 968\: {cm}^{2} + 1064.8 \: {cm}^{2} + 2 \times \pi \: {r}^{2} \\ \\ = > 2032.8 \: {cm}^{2} + 2 \times \frac{22}{7} \times ( {Outer Radius }^{2} - {Inner Radius}^{2} ) \\ \\ = > 2032.8 \: {cm}^{2} + 2 \times \frac{22}{7} \times ( {2.2}^{2} - {2}^{2} ) \\ \\ = > 2032.8 \: {cm}^{2} + 2 \times \frac{22}{7} \times (4.84 - 4) \\ \\ = > 2032.8 \: {cm}^{2} + 2 \times \frac{22}{7} (0.84) \\ \\ = > 2032.8 \: {cm}^{2} +2 \times \frac{22}{7} \times 0.84 \\ \\ = > 2032.8 \: {cm}^{2} + 2 \times \frac{22}{\cancel {7}} \ \times \cancel {0.84} \\ \\ = > 2032.8 \: {cm}^{2} + 2 \times 22 \times \: 0.12 \\ \\ = > 2032.8 \: {cm}^{2} + 2 \times 2.64 \\ \\ = > {2032.8 \: cm}^{2} + 5.28 \\ \\ = > 2038.08 \: {cm}^{2}$

Hence the answer is :-

(i) Inner curved surface area,

Answer = > 968 cm²

(ii) Outer curved surface area

Answer = > 1064.8 cm²

(iii) Total surface area.

Answer = > 2038.08 cm²

Hope it's helpful for you !!!