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 Fig. 13.11). Find its
(i) inner curved surface area,
(ii) outer curved surface area,
(iii) total surface area.

Answer 1

(i) inner curved surface area

According to the question inner diameter is 4 cm,

then,

Inner radius of a cylindrical pipe $=r_1=\frac{innnerdiameter}{2}=\left(\frac{4}{2}\right)cm=2cm$

Height (h) of cylindrical pipe=77 cm,

Curved Surface Area of inner surface of pipe $=2\pi r_{1}h$

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

$=968c{m}^2$

(ii) Outer curved surface area

According to the question outer diameter is 4.4 cm

Outer radius of cylindrical pipe $=r_2=\frac{outerdiamterer}{2}=\left(\frac{4.4}{2}\right)cm=2.2cm$

Height of cylinder = h = 77 cm,

Curved area of outer surface of pipe = $2\pi r_{2}h$

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

$=\left(2\times 22\times 2.2\times 11\right)c{m}^2$

$=1064.8c{m}^2$

(iii) Total surface area

Total surface area = curved surface area of inner cylinder + curved surface of outer cylinder + 2 $\times$ Area of base

Area of base = area of circle with radius 2.2 cm - Area of circle with radius 2 cm

$=\pi {r_2}^2-\pi {r_1}^2$

$=\frac{22}{7}\times ((2.2{)}^2-(2{)}^2)$

$=\frac{22}{7}\times (4.84-4)$

$=\frac{22}{7}\times \left(0.84\right)$

$=2.74c{m}^2$

Total surface area = curved surface area of inner cylinder + curved surface area of outer cylinder + 2 $\times$ Area of base

$=968+1064.8+2\times 2.74$

$=$ 2032.8 + 5.76

$=2039.08c{m}^2$

Therefore, the total surface area of the cylindrical pipe is

$=2039.08c{m}^2$