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# If θ is the angle (in degrees) of a sector of a circle of radius r, then area of the sector is

a. πr²θ/360

b. πr²θ/180

c. 2πrθ/360

d. 2πrθ/360

**Solution:**

Given, angle of a sector of a circle is θ

__Radius of the circle__ is r.

We have to find the __area of the sector__.

A sector is a part of a circle made of the arc of the circle along with its two radii.

It is a portion of the circle formed by a portion of the __circumference__ (arc) and radii of the circle at both endpoints of the arc

Area of whole 360° circle = πr²

Now, area of θ out of 360° of a circle = (θ/360°)πr²

Therefore, area of sector is πr²θ/360°

**✦ Try This: **If the angle of a sector of a circle of radius 5 cm is 60°, then area of the sector is

Given, angle of the sector, θ = 60°

Radius of the circle, r = 5 cm

We have to find the area of the sector.

Area of the sector = πr²θ/360°

= (22/7)(5)²(60°/360°)

= (22/7)(25)(1/6)

= (11/7)(25/3)

= 13.09 square cm.

Therefore, the area of the sector is 13.09 square cm.

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

**NCERT Exemplar Class 10 Maths Exercise 11.1 Sample Problem 2**

## If θ is the angle (in degrees) of a sector of a circle of radius r, then area of the sector is a. πr²θ/360, b. πr²θ/180, c. 2πrθ/360, d. 2πrθ/360

**Summary:**

If θ is the angle (in degrees) of a sector of a circle of radius r, then area of the sector is πr²θ/360°

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