Question

a metal of a pipe is 77cm long inner diameter is 4 cm outer diameter is 4.4cm.find TSA of hollow pipe ​

Answer 1

Answer:

• Height = 77 cm
• Inner Diameter = 4 cm
• Outer Diameter = 4.4 cm
• Inner Radius = 4/2 = 2 cm
• Outer Radius = 4.4/2 = 2.2 cm

Let Outer radius be 'R' cm , Inner radius be 'r' cm and Height be 'h' cm.

To calculate Total Surface area we have to calculate first :

(I) Area of top and bottom rings = 2[π(R² - r²)]

→ Area of top and bottom rings = 2 [22/7 (2.2² - 2²)]

→ Area of top and bottom rings = 2 × 22/7 × (2.2 + 2) (2.2 - 2)

→ Area of top and bottom rings = 2 × 22/7 × (4.2 × 0.2)/ (10 × 10)

→ Area of top and bottom rings = (2 × 22 × 6 × 2)/100

→ Area of top and bottom rings = 528/100

→ Area of top and bottom rings = 5.28 cm²

___________________...

(II) Inner Surface Area = 2πrh × h

⇢ Inner surface area = 2 × 22/7 × 2 × 77

⇢ Inner surface area = 88 × 11

⇢ Inner surface area = 968 cm²

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(III) Outer Surface Area = 2πR × h

➝ Outer Surface Area = 2 × 22/7 × 2.2 × 77

➝ Outer Surface Area = 2 × 22 × 2.2 × 11

➝ Outer Surface Area = 484 × 2.2

➝ Outer Surface Area = 1064.8 cm²

___________________...

Now, we can calculate the TSA of hollow pipe :

᠉ Total Surface Area = Area of top and bottom rings + Inner surface area + Outer surface area

᠉ Total Surface Area = 5.28 + 968 + 1064.8

᠉ Total Surface Area = 2038.08 cm²

Therefore, the TSA of hollow pipe is 2038.08 cm².

Answer 2

$\sf \color{red}Dimension \: \: b e : -$

$\sf \: R = outer \: radius \: = \frac{4.4}{2} = 2.2cm$

$\sf \:r = inner \: radius = \frac{4}{2} = 2 cm$

$\sf \: Height = 77 \: cm$

$\sf \colour{red} (i) Inner curve surface area = S_1 = 2 π rh$

$\sf = 2 × \frac{22}{7}\: × \: 2 \:× \:77{/tex} [tex] \underline{\boxed{\sf = 968 \: {cm}^{2} }}$

$\color{red} \sf \: (ii) \: outer \: curved \: surface \: area \: = S_2 = 2π R \times h$

$\sf \:2 \times \frac{22}{7} \times 2.2 \times 77$

$\underline{ \boxed{ \sf1064.8 \: {cm}^{2} }}$

$\color{red} \sf \: (iii) \: Total \: surface \: area = S_1 + S_2 + 2 \times \bigg[Rings are \bigg]$

$\sf = 968 \: {cm}^{2} + 10648 \: {cm}^{2} + 2 \bigg[π {R}^{2} -π {r}^{2} \bigg]$

$\sf \: 968 + 1064.8 + 2π \: \frac{22}{7} \bigg[ \big(2 - 2 { \big)}^{2} - \big(2 { \big)}^{2} \bigg]$

$\sf \: = 968 + 1064.8 + 5.28 cm$

$\underline{ \boxed{\sf = \: 2038.08 \: {cm}^{2} }}$