# 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 .

solution:   $R=$External radious $=$$12$.5 c

$\Rightarrow$          $r=$Internal radious$=$External radius - thickness) = ($12$.5 - 1)$=$11.5 c

$\Rightarrow$         h$=$Length of the pipe$=$20 cm

$\therefore$             Total surface areaof the pipe  $=$

(External curved surface)+(Internal curver surface) + 2(Area of the base of the ring)

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

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

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

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

$=2\times \frac{22}{7}\times (12.5+11.5) \times (20+12.5-11.5)cm^2=2\times\frac{22}{7} \times 24\times21 cm^2$

$=3168 cm^2$

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