Question

A metal pipe is 77 cm long. The inner diameter of its cross section is 2 cm ; the outer diameter is 2.2 cm. Find it's
1) inner curved surface area
2) outer curved surface area
3)Total surface area​

Answer 1

Step-by-step explanation:

Given:

• Length or height of pipe is 77 cm.
• Inner diameter of cross section is 2 cm.
• Outer diameter of cross section is 2.2 cm.

To Find:

• Inner csa
• Outer csa
• TSA

Solution: A pipe will have two layers there is a inner Cylinder and Outer Cylinder. Let inner radius be r and outer radius be R.

➟ r = Inner Diameter/2

➟ r = 2/2 = 1 cm

and

➟ R = Outer diameter/2

➟ R = 2.2/2 = 1.1 cm

As we know that

★ CSA of Cylinder = 2πrh ★

$\implies{\rm }$ Inner CSA = 2(22/7)(1)(77)

$\implies{\rm }$ 44(11)

$\implies{\rm }$ 484 cm²

So inner CSA is 484 cm².

Now, outer CSA = 2πRh

$\implies{\rm }$ Outer CSA = 2(22/7)(1.1)(77)

$\implies{\rm }$ 44(1.1)(11)

$\implies{\rm }$ 532.4 cm²

So outer CSA is 532.4 cm²

➬ TSA = Inner csa + Outer csa + 2π(Cross section surface area)

➬ TSA = 484 + 532.4 + 2(22/7)(R² – r²)

➬ 1016.4 + 44/7(1.1² – 1²)

➬ 1016.4 + 44/7(1.21 – 1)

➬ 1016.4 + 44/7(0.21)

➬ 1016.4 + 44(0.03)

➬ 1016.4 + 1.32

➬ 1017.72

Hence, TSA will be 1017.72 cm²

Answer 2

Step-by-step explanation:

$\bf {\underline {\underline \red{Given:-}}}$

• The height of the metal pipe = 77cm

• The inner diameter of its cross section is 2cm

• The outer diameter = 2.2cm

$\bf {\underline {\underline \blue{To\:Find:-}}}$

• The inner surface area of the pipe

• Outer curved surface area

• Total surface area of the pipe

$\bf {\underline {\underline \green{Solution:-}}}$

Inner diameter = 2cm

$\sf \: Inner \: radius \: r_{1} = \dfrac{2}{2} = 1cm$

Outer diameter = 2.2cm

$\sf \: Outer \: radius \: r_{2} = \dfrac{2.2}{2} = 1.1cm$

Height = 77cm

(i) Inner curved surface area

$\boxed{\sf Inner \: curved \: surface \: area = 2\pi r_{1}h }$

$\sf \longrightarrow2 \times \dfrac{22}{7} \times 1 \times 77$

$\sf \longrightarrow2 \times {22} \times 1 \times 11$

$\sf\longrightarrow44 \times 11$

$\sf\longrightarrow484 {cm}^{2}$

(ii) Outer curved surface area

$\boxed{\sf Outer\: curved \: surface \: area = 2\pi r_{2}h }$

$\sf \longrightarrow2\times \dfrac{22}{7} \times 1.1 \times 77$

$\sf \longrightarrow2 \times {22} \times 1.1 \times 11$

$\sf\longrightarrow44 \times 12.1$

$\sf\longrightarrow532.4 {cm}^{2}$

(iii) Total surface area of the metal pipe

Total surface area of pipe = Inner curved surface + Outer curved surface area + Area of circular base and top

$\sf\longrightarrow484 + 532.4 + 2\pi \{( { r_{2} )}^{2} - { (r_{1}) }^{2} \}$

$\sf\longrightarrow1016.4 + 2\pi \{( { 1.1)}^{2} - { (1) }^{2} \}$

$\sf\longrightarrow1016.4 + 2\pi ( 1.21 - 1 )$

$\sf\longrightarrow1016.4 + 2 \times \dfrac{22}{7} \times 0.21$

$\sf\longrightarrow1016.4 +1.32$

$\sf\longrightarrow1017.72 {cm}^{2}$

Therefore:-

• Inner curved surface area = 484cm²

• Outer curved surface area = 532.4cm²

• Total surface area = 1017.72cm²