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# The central angles of two sectors of circles of radii 7 cm and 21 cm are respectively 120° and 40°. Find the areas of the two sectors as well as the lengths of the corresponding arcs. What do you observe

**Solution:**

Given, radii of two circles are 7 cm and 21 cm

Central angle of the two angles are 120° and 40°

We have to find the areas of the sectors as well as the lengths of the corresponding arcs.

Considering radius = 7 cm and central angle = 120°

Area of sector = πr²θ/360°

= (22/7)(7)²(120°/360°)

= (22)(7)(1/3)

= 154/3

= 51.33 cm²

Length of the arc = θ/360°(2πr)

= (120°/360°)(2)(22/7)(7)

= (1/3)(44)

= 44/3

= 14.67 cm²

Considering radius 21 cm and central angle = 40°

Area of sector = (22/7)(21)²(40°/360°)

= (22)(3)(21)(1/9)

= (22)(21)(1/3)

= (22)(7)

= 154 cm²

Length of the arc = θ/360°(2πr)

= (40°/360°)(2)(22/7)(21)

= (1/9)(44/7)(21)

= (1/9)(44)(3)

= 44/3

= 14.67 cm²

Therefore, we observe that the length of the arc of two circles are equal but the area of the sectors are not equal.

**✦ Try This: **The central angles of two sectors of circles of radii 9 cm and 28 cm are respectively 100° and 60°. Find the areas of the two sectors as well as the lengths of the corresponding arcs. What do you observe?

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 12

**NCERT Exemplar Class 10 Maths Exercise 11.4 Problem 16**

## The central angles of two sectors of circles of radii 7 cm and 21 cm are respectively 120° and 40°. Find the areas of the two sectors as well as the lengths of the corresponding arcs. What do you observe

**Summary:**

The central angles of two sectors of circles of radii 7 cm and 21 cm are respectively 120° and 40°. The areas of the two sectors are 51.33 cm² and 154 cm². The lengths of the corresponding arcs are 14.67 cm². We observe that the length of the arc of two circles are equal but the area of the sectors are not equal

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