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 (see figure). Find its
(i) Inner curved surface area.
(ii) Outer curved surface area
(iii) Total surface area

Answer 1

Given:

Inner radius $=\frac{4}{2}=2$ cm $=r_1$

Outer radius $=\frac{4.4}{2}=2.2$cm $=r_2$

Height $=77$ cm

Solution:

(i) Curved Surface Area $=2\pi r_{1}h$ (inner)
$=2\times \frac{22}{7}\times 2\times 77=968$ cm${}^2$

(ii) Outer Curved Surface Area (outer)$=2\pi r_{2}h$
$=2\times \frac{22}{7}\times 2.2\times 77{cm}^2=(22\times 22\times 2.2)$ cm${}^2$
$=1064.8{cm}^2$

(iii) Total Surface Area of pipe $=$ CSA of inner surface $+$ CSA of outer surface $+$ Area of circular base and top
$=968+1064.8+2\pi ({\left(2.2\right)}^2-{\left(2\right)}^2)$
$=2032.8+5.28$ cm${}^2$
$=2038.08$ cm${}^2$