Question

An iron pipe $20cm$ long has exterior diameter equal to $25cm$. if the thickness of the pipe is $1cm$, find the whole surface area of the pipe.

Answer 1

The pipe is $20cm$ long $\left(l\right)$

extension diameter is $25cm$, thickness is $10m$.

$\therefore$ exterior radius $\left(R\right)=\frac{25}{2}cm$

interior radius $\left(r\right)=\frac{25}{2}-1=\frac{23}{2}cm$

So, the total surface area is

$=$ exterior surface of the pipe $+$

interior surface of the pipe $+$

two ends of the pipe (thickness area)

$=2\pi \left(R\right).l+2\pi \left(r\right).l+2(\pi r^2-\pi r^2)$

$=2\pi \left[l\right(R+r)+(R+r\left)\right(R-r\left)\right]$

$=2\pi (R+r)(l+R-r)$

$=2\times \frac{22}{7}\times (\frac{25}{2}+\frac{23}{2})(20+\frac{25}{2}-\frac{23}{2})$

$=\frac{44}{7}\times 24\times 21$

$=44\times 72$

$=3168$

So, the total surface face area is 3168 sq.cm.