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

Solution(By Examveda Team)

External radius, R = $$\frac{{25}}{2}$$ cm
Internal radius, r $$ = \left( {\frac{{25}}{2} - 1} \right){\text{cm}}$$   $$ = \frac{{23}}{2}{\text{ cm}}$$
Length, h = 20 cm
Whole surface area :
$$\eqalign{ & = 2\pi Rh + 2\pi rh + 2\pi \left( {{R^2} - {r^2}} \right) \cr & = 2\pi \left[ {\left( {R + r} \right)h + \left( {{R^2} - {r^2}} \right)} \right] \cr} $$
$$ = 2 \times \frac{{22}}{7} \times $$ $$\left[ {\left( {\frac{{25}}{2} + \frac{{23}}{2}} \right) \times 20 + \left( {\frac{{25}}{2} + \frac{{23}}{2}} \right)\left( {\frac{{25}}{2} - \frac{{23}}{2}} \right)} \right]$$        $${\text{ c}}{{\text{m}}^2}$$
$$\eqalign{ & = \left( {2 \times \frac{{22}}{7} \times 504} \right){\text{ c}}{{\text{m}}^2} \cr & = 3168{\text{ c}}{{\text{m}}^2} \cr} $$