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

Explanation

Length of the pipe, `h = 20 cm`
External radius of the pipe, `R = (25)/(2) cm = 12.5 cm`
Thickness of the pipe `= 1 cm`
Internal radius of the pipe, `r = (12.5 -1) cm = 11.5 cm`
Total surface area of the pipe
= (external curved surface area) + (internal curved surface area) + 2(area of the base ring)
`= [2pi Rh + 2pi rh + 2(pi R^(2) - pi r^(2))]` sq units
`[2pi h (R + r) + 2pi (R^(2) - r^(2))]` sq units
`= 2pi (R + r) [h + (R - r)]` sq units
`= 2 xx (22)/(7) xx (12.5 + 11.5) (20 + 12.5 - 11.5) cm^(2)`
`= (2 xx (22)/(7) xx 24 xx 21) cm^(2) = 3168 cm^(2)`
Hence, the total surface area of the pipe is `3168 cm^(2)`