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

Explanation

Height of pipe`=20cm`
External diameter`=25 cm`
External radius,
`R=25/2=12.5 cm`
The thickness of the pipe`=1 cm`
Therefore, Internal radius:
`r=12.5−1=11.5 cm`
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
`=2piRh+2pirh+pi(R^2−r^2)+pi(R^2−r^2)`
`=2pih(R+r)+2pi(R^2−r^2)`
`=2xx2/7xx[20(12.5+11.5)+(12.5)^2−(11.5)^2] cm^2`
`=447[20xx24+(12.5−11.5)(12.5+11.5)] cm^2` `[∵(a^2−b^2)=(a−b)(a+b)]`
`=44/7[480+24] cm^2`
`=44/7[504]cm^2`
`=44xx72 cm^2`
`=3168 cm^2`
So, the total surface area of the pipe is `3168cm^2`.