Question

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

Answer 1

h=77cm
r₁=4.4cm
r₂=4cm

now find l²=h²+(r₁-r₂)²=5929+0.16=5929.16
so, l=70

now all we have to do is to use this:
"πl(r₁+r₂)+πr₁²+πr₂²"
=[3.14*70*(8.4)]+[3.14*19.36]+[3.14*16]
=1848+60.85+50.29
=1959.14

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.

_____________________

$\rm \odot \: Inner \: Radius \: (r) = \dfrac{Diameter}{2} = \dfrac{4}{2} = \green { \bold{2 \: cm} }$

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

_____________________

As we know,

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

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

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

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

$\rm \longrightarrow 44 \times 22$

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

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

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

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

$\rm \longrightarrow 44 \times 24.2$

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

_____________________

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