Question

a metallic pipe is 70cm long.the inner diameter of cross section is 3.5cm and outer diameter is 4.2cm.find its TSA.

Answer 1

Answer :-

• TSA of Pipe = 1702.47 cm²

Given :-

• Length (Here Height) of Pipe = 70 cm
• Inner Diameter = 3.5 cm
• Outer Diameter = 4.2 cm

To Find :-

• TSA of Pipe = ?

Explanation :-

In Order to Find the TSA of the Pipe, First we need to find the Inner and Outer CSA.

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$\rm \odot \: Inner \: Radius \: (r) = \dfrac{Diameter}{2} = \dfrac{3.5}{2} = \green { \bold{1.75 \: cm} }$

$\rm \odot \: Outer \: Radius \: (R) = \dfrac{Diameter}{2} = \dfrac{4.2}{2} = \green { \bold{2.1 \: cm} }$

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As we know,

$\blue { \boxed { \bf \bigstar \: CSA \: of \: Cylinder = 2 \pi rh \: \bigstar }}$

$\bf 1. \: \underline { Inner \: CSA = 2 \pi rh }$

$\rm \longrightarrow 2 \times \dfrac{22}{7} \times 1.75 \times 70$

$\rm \longrightarrow 2 \times 22 \times 1.75 \times 10$

$\rm \longrightarrow 44 \times 17.5$

$\orange { \boxed { \bf \longrightarrow 770 \: cm^2 }}$

$\bf 2. \: \underline { Outer \: CSA = 2 \pi Rh }$

$\rm \longrightarrow 2 \times \dfrac{22}{7} \times 2.1 \times 70$

$\rm \longrightarrow 2 \times 22 \times 2.1 \times 10$

$\rm \longrightarrow 44 \times 21$

$\orange { \boxed { \bf \longrightarrow 924 \: cm^2 }}$

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Now Finding TSA of Pipe,

$\blue { \boxed { \bf \bigstar \: TSA \: of \: Pipe = Inner \: CSA + Outer \: CSA + Area \: of \: 2 \: Bases \: \bigstar }}$

$\rm : \: \longrightarrow 2 \pi rh + 2 \pi Rh + 2 \pi (R^2 - r^2)$

$\rm : \: \longrightarrow 770 + 924 + [ 2 \times \dfrac{22}{7} (2.1^2 - 1.75^2) ]$

$\rm : \: \longrightarrow 1694 + 2 \times \dfrac{22}{7} (4.41 - 3.0625)$

$\rm : \: \longrightarrow 1694 + 2 \times \dfrac{22}{7} \times 1.3475$

$\rm : \: \longrightarrow 1694 + 44 \times 0.1925$

$\rm : \: \longrightarrow 1694 + 8.47$

$\red { \underline { \boxed { \bf : \: \longrightarrow 1702.47 \: cm^2 }}}$

Hence, the TSA of the pipe is 1702.47 cm²