an iron pipe 20 cm long has external diameter equal to 25 cm if the thickness of the pipe - Maths -

Question

an iron pipe 20 cm long has external diameter equal to 25 cm if
the thickness of the pipe is 1 cm, find the whole surface of the
pipe

Lalit Mehra · Accepted Answer

Let r and R be the inner and outer radius of the iron pipe respectively.

Height of the pipe, h = 20 cm.

Given, 2R = 25 cm

$∴ R = \frac{25}{2} cm$

Thickness of the pipe = R – r

∴ R – r = 1 cm (Given)

$\Rightarrow \frac{25}{2} cm - r = 1 cm \Rightarrow r = \frac{25}{2} cm - 1 cm = \frac{23}{2} cm$

Total surface area of the pipe

= 2 $π$ (R – r) h + 2 $π$ (R² – r²)

= 2 $π$ (R – r) [h + (R – r)]

$= 2 \times \frac{22}{7} \times 1 cm × (20 + \frac{25}{2} + \frac{23}{2}) cm = 2 \times \frac{22}{7} \times (20 + 24) {cm}^{2} = 2 \times \frac{22}{7} \times 44 {cm}^{2} = \frac{1936}{7} {cm}^{2}$

Thus, the total surface area of the pipe is $\frac{1936}{7} {cm}^{2}$ .

2

an iron pipe 20 cm long has external diameter equal to 25 cm. if the thickness of the pipe is 1 cm, find the whole surface of the pipe