Question

a metal pipe is 70cm long. the inner diameter of a cross section is 4cm and the outer diameter is 4.8cm. Find the total surface area.​

Answer 1

Answer :-

• TSA of Pipe =  1947 cm²         [Approx.]

Given :-

• Length (Here Height) of Pipe = 70 cm
• Inner Diameter = 4 cm
• Outer Diameter = 4.8 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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$\rm \odot \: Inner \: Radius \: (r) = \dfrac{Diameter}{2} = \dfrac{4}{2} = \green { \bold{2 \: cm} }$

$\rm \odot \: Outer \: Radius \: (R) = \dfrac{Diameter}{2} = \dfrac{4.8}{2} = \green { \bold{2.4 \: cm} }$

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As we know,

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

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

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

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

$\rm \longrightarrow 44 \times 20$

$\orange { \boxed { \bf \longrightarrow 880 \: cm^2 }}$

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

$\rm \longrightarrow 2 \times \dfrac{22}{7} \times 2.4 \times 70$

$\rm \longrightarrow 2 \times 22 \times 2.4 \times 10$

$\rm \longrightarrow 44 \times 24$

$\orange { \boxed { \bf \longrightarrow 1056 \: cm^2 }}$

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Now Finding TSA of Pipe,

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

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

$\rm : \: \longrightarrow 880 + 1056 + [ 2 \times \dfrac{22}{7} (2.4^2 - 2^2) ]$

$\rm : \: \longrightarrow 1936 + 2 \times \dfrac{22}{7} (5.76 - 4)$

$\rm : \: \longrightarrow 1936 + \dfrac{44}{7} \times 1.76$

$\rm : \: \longrightarrow 1936 + 11 \qquad [Approx.]$

$\red { \underline { \boxed { \bf : \: \longrightarrow 1947 \: cm^2 \qquad [Approx.] }}}$

Hence, the TSA of the pipe is 1947 cm² [Approx]