Question

a metal pipe is 77cm long.the inner diameter of cross section is 4cm and the outer diameter is 4.4cm . find its total surface area

Answer 1

We have, R = external radius =4.4/2 cm=2.2 cmr = internal radius =42cm=2cmh = length of the pipe = 77 cm Total surface area of a pipe= Inner curved surface area + outer curved surface area + areas of two bases= 2πrh+2πRh+2π(R2−r2)= [968+1064.8+2×227(4.84−4)] cm²= (2032.8+447×0.84)cm²=(2032.8+5.28)cm²=2038.08cm²

Answer 2

Answer :-

• TSA of Pipe =  2038.08 cm²

Given :-

• Length (Here Height) of Pipe = 77 cm
• Inner Diameter = 4 cm
• Outer Diameter = 4.4 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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$\rm \odot \: Inner \: Radius \: (r) = \dfrac{Diameter}{2} = \dfrac{4}{2} = \green { \bold{2 \: cm} }$

$\rm \odot \: Outer \: Radius \: (R) = \dfrac{Diameter}{2} = \dfrac{4.4}{2} = \green { \bold{2.2 \: cm} }$

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As we know,

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

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

$\rm \longrightarrow 2 \times \dfrac{22}{7} \times 2 \times 77$

$\rm \longrightarrow 2 \times 22 \times 2 \times 11$

$\rm \longrightarrow 44 \times 22$

$\orange { \boxed { \bf \longrightarrow 968 \: cm^2 }}$

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

$\rm \longrightarrow 2 \times \dfrac{22}{7} \times 2.2 \times 77$

$\rm \longrightarrow 2 \times 22 \times 2.2 \times 11$

$\rm \longrightarrow 44 \times 24.2$

$\orange { \boxed { \bf \longrightarrow 1064.8 \: cm^2 }}$

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Now Finding TSA of Pipe,

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

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

$\rm : \: \longrightarrow 968 + 1064.8 + [ 2 \times \dfrac{22}{7} (2.2^2 - 2^2) ]$

$\rm : \: \longrightarrow 2032.8 + 2 \times \dfrac{22}{7} (4.84 - 4)$

$\rm : \: \longrightarrow 2032.8 + \dfrac{44}{7} \times 0.84$

$\rm : \: \longrightarrow 2032.8 + 5.28$

$\red { \underline { \boxed { \bf : \: \longrightarrow 2038.08 \: cm^2 }}}$

Hence, the TSA of the pipe is 2038.08 cm²