Question

find the inner curved surface area of a metal pipe which is 77 cm long the inner diameter is 4cm and outer diameter is 4.4cm

Answer 1

Answer:

Step-by-step explanation:

Inner curved surface area=2πrh

Radius=4/2=2cm

2π*2*77

968

Answer 2

Answer

Inner surface = 968 cm²

Outer curved surface area = 1064.8 cm² [not asked]

Total surface area = 1984.4cm²

Step-by-step-explaination

Let R and r be the outer and inner radii of the metal pipe.

R = 2.2cm

r = 2cm

Length of the metal pipe = 77cm

Finding inner curved surface area:-

Inner curved surface area of metallic pipe = 2 π r h

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: 2 \times \dfrac{22}{7} \times 77$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: 88 \times {11cm}^{2}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: 44 \times 2.2 \times 11 {cm}^{2}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: 1064.8 {cm}^{2}$

Finding outer curved surface area :

Outer curved surface area = 2 π R h

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: 2 \times \dfrac{22}{7} \times 2.2 \times 77 {cm}^{2}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: 44 \times 2.2 \times 11 {cm}^{2}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: 1064.8 {cm}^{2}$

Finding total surface area :

Total surface area = Inner CSA + Outer CSA + Area of bases

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: icsa + ocsa + 2( \pi - {R}^{2} - \pi {r}^{2} )$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies968 + 1064.8 + 2 \times \dfrac{22}{7} \{(2.2 {)}^{2} - {2}^{2} \}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: 968 + 1064.8 + 5.28 {cm}^{2}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: 2038.08 {cm}^{2}$

Total surface area = Inner CSA + Outer CSA

Total surface area = 968 + 1016.4cm²

Total surface area = 1984.4cm²