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

To find inner curved surface area:

Radius of inner curved surface $R_1=\frac{\text{inner diameter}}{2}$
$=\frac{4}{2}$
$R_1=2cm$

Height of the pipe $\left(h\right)=77cm$

surface area of inner curved surface$=2\pi R_{1}h$
$=2\times \frac{22}{7}\times 2\times 77$
$=4\times 22\times 11$
$=968c{m}^2$
To find outer curved surface area:

Radius of outer curved surface$R_2=\frac{\text{outer diameter}}{2}$
$=\frac{4.4}{2}$
$\therefore R_2=2.2cm$

Height of the pipe$=77cm$

Surface area of outer curved surface$=2\pi R_{2}h$
$=2\times \frac{22}{7}\times 2.2\times 77$
$=2\times 22\times 2.2\times 11$
$=1064.8c{m}^2$

Total surface area$=$ inner curved surface area$+$outer curved surface area$+2\times$ area of base
area of base$=$ area of circle with radius $2.2-$ area of circle with radius $2$
$=\pi \left[\right(R_2{)}^2-\left(R_1{)}^2\right]$
$=\pi \left[\right(2.2{)}^2-2^2]$
$=\pi [4.84-4]$
$=\frac{22}{7}\times 0.84$

$=2.64c{m}^2$

​​​​​​Total surface area$=968+1064.8+(2\times 2.64$)
$=2032.8+5.28$

$=2038.08c{m}^2$

Therefore, Total surface area $=2038.08c{m}^2$