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 :

Answer: Option B

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 :
$$\begin{array}{rl}& =2\pi Rh+2\pi rh+2\pi \left(R^2-r^2\right)\\ & =2\pi \left[\left(R+r\right)h+\left(R^2-r^2\right)\right]\end{array}$$
$$=2\times \frac{22}{7}\times$$ $$\left[\left(\frac{25}{2}+\frac{23}{2}\right)\times 20+\left(\frac{25}{2}+\frac{23}{2}\right)\left(\frac{25}{2}-\frac{23}{2}\right)\right]$$        $$\text{ c}{\text{m}}^2$$
$$\begin{array}{rl}& =\left(2\times \frac{22}{7}\times 504\right)\text{ c}{\text{m}}^2\\ & =3168\text{ c}{\text{m}}^2\end{array}$$