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

Given :

Length $=77cm$,

Inner diameter $=4cm$, hence inner radius $\left(r\right)$$=2cm$

outer daimeter $=4.4cm$, hence outer radius $\left(R\right)$ $=2.2cm$

Height of the pipe $=length$

$\Rightarrow$Inner surface area ( inner CSA) $=$ $2\pi$$rh$

$\Rightarrow$ Inner CSA $=$ $2\times \frac{22}{7}\times 2\times 77$

$\Rightarrow$Inner CSA $=$ $968c{m}^2$

Outer CSA$=$ $2\pi$$Rh$

$\Rightarrow$Outer CSA $=$ $2\times \frac{22}{7}\times 2.2\times 77$

$\Rightarrow$Outer CSA$=$ $1064.8c{m}^2$

Now the total surface area on the ends $=$ $2\pi (R-r)(R+r)$

$\Rightarrow 2\times \frac{22}{7}\times 4.2\times 0.2$

$\Rightarrow 5.28$ cm

The total surface area$=$outer CSA + Inner CSA + TSA on the ends

The total surface area $=$ $1068.8+968+5.28$

The toal surface area $=$ $2038.08$ $c{m}^2$