Question

A metal pipe is 77cm long the inner diameter of the cross section is 4 cm and the outer diameter is 4.8 cm find the total surface area.​

Answer 1

A metal pipe is 77cm long the inner diameter of the cross section is 4 cm and the outer diameter is 4.8 cm find the total surface area.

Solution:-

A metal pipe is = 77cm

The inner diameter of the cross section is = 4 cm

The outer diameter is = 4.8 cm

Total surface area : ?

π ( r2² - r1² ) + 2 π l ( r1 + r2 )

[ Putting the value in the equation ]

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Total area of cross section is = 4279 . 6 cm ² .

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Answer 2

Given,

Length of metal pipe ($l$) $=77cm$.

Diameter of inner section is $4cm$.

So, radius of inner section $(r_{1}) = \frac {4} {2} = 2cm$.

Diameter of outer section is $4.8cm$.

So, radius of outer section $(r_{2})=\frac {4.8} {2} =2.4cm$.

We know that, total surface area $=$ Curved surface area of inner section $+$ Curved surface area of outer section $+(2\times$ area of the base).

(i) curved surface area of inner section:

Formula: Curved surface area $=2\pi r_{1}l$

$=2\times 3.14 \times 2\times 77$

$=967.12cm^{2}$.

(ii) Curved surface area of outer section:

Formula: $2\pi r_{2}l$

$=2\times 3.14 \times 2.4\times 77$

$=1160.54cm^{2}$.

(iii) Area of base:

We know that area of base $=$Area of outer section $-$ Area of inner section.

Area of section (circle) $=\pi r^{2}$.

Area of base $=\pi r_{2}^{2} -\pi r_{1}^{2}$

$=(3.14\times (2.4)^{2} ) -(3.14\times(2)^{2} )$

$=(3.14\times5.76)-(3.14\times4)$

$=18.055-12.56$

$=5.495cm^{2}$.

So, Total surface area $=967.12+1160.54+(2\times5.495)$

$=967.12+1160.54+10.99$

$=2136.65cm^{2}$.

Hence, total surface area of the given metal pipe is $2138.65cm^{2}$.