Question

A metal pipe is 77 cm77 cm long. The inner diameter of a cross-section is 4 cm4 cm, the outer diameter being 4.4 cm4.4 cm, then find its total surface area.

Answer 1

Dimensions be :

$\Rightarrow R=$ Outer radius $=\frac{4.4}{2}=2.2cm$

$r=$ Inner radius $\frac{4}{2}=2cm$

Height $h=77cm$

$\Rightarrow$ Inner curved surface area $=2\pi rh$

$=2\times \frac{22}{7}\times 2\times 77$

$=968c{m}^2$

$\Rightarrow$ Outer curved surface area $=2\pi Rh$

$=2\times \frac{22}{7}\times 4.2\times 77$

$=1064.8c{m}^2$

$\Rightarrow$ Total surface area $=968+1064.8+2\pi \times Rin{g}^{\prime }sarea$

$=968+1064.8+2\times [\pi R^2-\pi r^2]$

$=968+1064.8+2\times [\frac{22}{7}\times {\left(2.2\right)}^2-\frac{22}{7}\times {\left(2\right)}^2]$

$=968+1064.8+2\times \frac{22}{7}\times [{\left(2.2\right)}^2-{\left(2\right)}^2]$

$=968+1064.8+5.28$

$=2038.08$

$\Rightarrow$ Total surface area $=2038.08c{m}^2.$

Hence, the answer is $2038.08c{m}^2.$