Question

The angle of a sector is 30 .If its radius is 42 cm ,them the length of the arc of the sector is

Answer 1

Answer:

22 cm

Step-by-step explanation:

Given:

Angle of sector (∅) = 30°

Radius (r) = 42 cm

To find:

The length of the arc

Solution:

As we know length of arc = 2πr × ∅/360

So,

$= 2\pi r \times \frac{ \theta}{360 \degree} \\ \\ = 2 \times \frac{22}{7} \times 42 \times \frac{30\degree}{360 \degree } \\ \\ = 2 \times 22 \times 6 \times \frac{1}{12} \\ \\ = 22 \times 12 \times \frac{1}{12} \\ \\ = 22 \\ \\ \therefore \text{The required length of arc is 22 cm}$

Important Points

Arc: An arc is curved part of circle .

Sector : A sector is also a part of circle which consist two radius and an arc .

Formula Related to Arc and Sector

Let, r be the radius , ∅ (Angle NOM) be the angle .

Area of Sector = πr² × ∅/360°

Length of Arc = 2πr × ∅/360°