Question

An iron pipe $20cm$ long has exterior diameter $25cm$. If it's thickness is $1cm$ then find the whole surface area of the pipe.

Answer 1

Height of pipe $=20cm$

External diameter $=25cm$

External radius, $R=\frac{25}{2}=12.5cm$

The thickness of the pipe $=1cm$

therefore, Internal radius, $r=12.5-1=11.5cm$

Let the external radius be $R$ and the internal radius be $r.$

Then Total surface area of the pipe $=$ Outside surface area $+$ inside surface area $+$ Top Base Area $+$ bottom base area

$=2\pi Rh+2\pi rh+\pi (R^2-r^2)+\pi (R^2-r^2)$

$=2\pi h(R+r)+2\pi (R^2-r^2)$

$=2\times \frac{22}{7}\times \left[20\right(12.5+11.5)+(12.5{)}^2-({11.5}^2)]c{m}^2$

$=\frac{44}{7}[20\times 24+(12.5-11.5\left)\right(12.5+11.5\left)\right]c{m}^2$ $[\because (a^2-b^2)=(a-b\left)\right(a+b\left)\right]$

$=\frac{44}{7}[480+24]c{m}^2$

$=\frac{44}{7}\left[504\right]c{m}^2$

$=44\times 72c{m}^2$

$=3168c{m}^2$

So, the total surface area of the pipe is $3168c{m}^2$