Find the difference of the areas of a sector of angle 120° and its corresponding major sector of a circle of radius 21 cm
Solution:
Given, central angle = 120°
Radius of circle = 21 cm
We have to find the difference between the areas of a sector and corresponding major sector of a circle.
Considering circle with radius 21 cm
Area of circle = πr²
= (22/7)(21)²
= 1386 cm²
Considering sector AOBA
Area of a sector = πr²θ/360°
Area of minor sector AOBA = (22/7)(21)²(120°/360°)
= (22)(3)(21)(1/3)
= (22)21
= 462 cm²
Area of major sector = area of circle - area of minor sector
= 1386 - 462
= 924 cm²
Area of major sector and its corresponding major sector ABOA = area of major sector - area of minor sector
= 924 - 462
= 462 cm²
Therefore, the difference between the areas of a sector and corresponding major sector of a circle is 462 cm²
✦ Try This: Find the difference of the areas of a sector of angle 90° and its corresponding major sector of a circle of radius 32 cm.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12
NCERT Exemplar Class 10 Maths Exercise 11.4 Problem 20
Find the difference of the areas of a sector of angle 120° and its corresponding major sector of a circle of radius 21 cm
Summary:
The difference of the areas of a sector of angle 120° and its corresponding major sector of a circle of radius 21 cm is 462 cm²
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