# A metal pipe is 77 cm long.

Question. A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm.

(i) Inner curved surface area,

(ii) Outer curved surface area

(iii) Total surface area. $\left[\right.$ Assume $\left.\pi=\frac{22}{7}\right]$

Solution:

Inner radius $\left(r_{1}\right)$ of cylindrical pipe $=\left(\frac{4}{2}\right) \mathrm{cm}=2 \mathrm{~cm}$

Outer radius $\left(r_{2}\right)$ of cylindrical pipe $=\left(\frac{4.4}{2}\right) \mathrm{cm}=2.2 \mathrm{~cm}$

Height $(h)$ of cylindrical pipe $=$ Length of cylindrical pipe $=77 \mathrm{~cm}$

(i) CSA of inner surface of pipe $=2 \pi r_{i} h$

$=\left(2 \times \frac{22}{7} \times 2 \times 77\right) \mathrm{cm}^{2}$

$=968 \mathrm{~cm}^{2}$

(ii) CSA of outer surface of pipe $=2 \pi r_{2} h$

$=\left(2 \times \frac{22}{7} \times 2.2 \times 77\right) \mathrm{cm}^{2}$

$=(22 \times 22 \times 2.2) \mathrm{cm}^{2}$

$=1064.8 \mathrm{~cm}^{2}$

(iii) Total surface area of pipe $=$ CSA of inner surface $+\operatorname{CSA}$ of outer surface $+$ Area of both circular ends of pipe

$=2 \pi r_{1} h+2 \pi r_{2} h+2 \pi\left(r_{2}^{2}-r_{1}^{2}\right)$

$=\left[968+1064.8+2 \pi\left\{(2.2)^{2}-(2)^{2}\right\}\right] \mathrm{cm}^{2}$

$=\left(2032.8+2 \times \frac{22}{7} \times 0.84\right) \mathrm{cm}^{2}$

$=(2032.8+5.28) \mathrm{cm}^{2}$

$=2038.08 \mathrm{~cm}^{2}$

Therefore, the total surface area of the cylindrical pipe is $2038.08 \mathrm{~cm}^{2}$.