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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