Question

A metal pipe is 63 cm long ,its inner diameter is 4 cm and the outer diameter is 4.4 cm, then its inner curved surface area is

Answer 1

• The inner curved surface area (C.S.A.) of the metal pipe = 792 cm².

Given :

• The length of a metal pipe = 63 cm.
• The inner diameter of the metal pipe = 4 cm.
• The outer diameter of the metal pipe = 4.4 cm.

To Find :

• The inner curved surface area (C.S.A.) of the metal pipe.

Solution :

Given,

The length of the pipe (height) is 63 m.

The inner diameter of the metal pipe is 4 cm.

We know that,

Curved surface area (C.S.A.) of the cylindrical pipe = $\rm 2\pi r_{1} h$

We have,

Diameter of the pipe.

So, first we need to find the inner radius of the pipe.

We know that,

$\: \: \bullet \: \: \sf Radius \: (r_{1}) = \dfrac{Diameter}{2} \\ \\ : \implies \rm \dfrac{4}{2} \: cm \\ \\ : \implies \rm 2 \: cm \\ \\ \: \: \rm \therefore \: \: r_{1} = 2 \: cm$

Now,

$:\implies \rm 2 \times \dfrac{22}{7} \times 2 \: cm \times 63 \: cm \\ \\ :\implies \rm 2 \times 22 \times 2 \times 9 \: {cm}^{2} \\ \\ :\implies \rm 44 \times 18 \: {cm}^{2} \\ \\ :\implies \rm 792 \: {cm}^{2} \\ \\ \: \: \rm \therefore \: \: C.S.A. = 792 \: {cm}^{2}$

Hence,

The inner curved surface area (C.S.A.) of the metal pipe is 792 cm².

______________________________

Extra :

★ The outer curved surface area of the metal pipe.

we are given that, the outer curved surface area (C.S.A.) of the pipe. so, we can also find the outer curved surface area (C.S.A.).

We know that,

Curved surface area (C.S.A.) of the cylindrical pipe = $\rm2 \pi r_{2} h$

$\: \: \bullet \: \: \sf Radius \: (r_{2}) = \dfrac{Diameter}{2} \\ \\ : \implies \rm \dfrac{4.4}{2} \: cm \\ \\ : \implies \rm 2.2\: cm \\ \\ \: \: \rm \therefore \: \: r_{2} = 2.2 \: cm$

Now,

$:\implies \rm 2 \times \dfrac{22}{7} \times 2.2 \: cm \times 63 \: cm \\ \\ :\implies \rm 2 \times 22 \times 2.2 \times 9 \: {cm}^{2} \\ \\ :\implies \rm 44 \times 19.8 \: {cm}^{2} \\ \\ :\implies \rm 871.2 \: {cm}^{2} \\ \\ \: \: \rm \therefore \: \: C.S.A. = 871.2\: {cm}^{2}$

Hence,

The outer curved surface area of the pipe is 871.2 cm².