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

> Inner Surface area of the Pipe = 968 Square cm.

> Outer Surface area of the pipe = 1064.8 Square cm.

> Total Surface Area = = 2038.08 Square cm.

> Step-by-step explanation:

A pipe will have two layers as shown in picture.

There is a inner Cylinder and Outer Cylinder.

Inner Radius = Inner Diameter / 2 = 4 / 2 = 2 cm = r

Outer Radius = Outer Diameter / 2 = 4.4/2 = 2.2 cm = R

Height of the pipe = 77 cm = h

Inner Surface area of the Pipe = 2∏rh = 2*22*2*77/7 = 968 Square cm.

Outer Surface area of the pipe = 2∏Rh = 2*22*2.2*77/7 = 1064.8 Square cm.

Total Surface area = Inner Surface area + Outer Surface area + 2 * Cross section surface area.

The cross section suface area is present at two ends of the pipe.

This is the area covered between 2 circles.

Total Surface area = Inner Surface area + Outer Surface area + 2 * Cross section surface area.

= 968 + 1064.8 + 2*∏(R^2 – r^2)

= 2032.8 + 2*22*(2.2*2.2 – 2*2)/7

= 2032.8 + 5.28

= 2038.08 Square cm.

Answer 2

Inner radius of cylindrical pipe

$= r_{1} = \frac{ inner \: \: diameter}{2} = \binom{4}{2} cm = 2cm$

Hight

$(h)$

of cylindrical pipe =77cm

Curved surface Area of inner surface of pipe =

$2\pi \: r_{1}h$

$= (2 \times \frac{22}{7} \times 2 \times 77) {cm}^{2} \\ = 968 {cm}^{2}$