Example 1 - Chapter 11 Class 10 Areas related to Circles

Last updated at April 16, 2024 by Teachoo

Transcript

Example 1 (Method 1)
Find the area of the sector of a circle with radius 4 cm and of angle 30°. Also, find the area of the corresponding major sector (Use π = 3.14).
Given
Radius = r = 4 cm, θ=30°
Now,
Area of sector = 𝜽/𝟑𝟔𝟎 × 𝝅𝒓𝟐
= 30/360 × 3.14 × (4)2
= 𝟏/𝟏𝟐 × 𝟑.𝟏𝟒 × 𝟒 × 𝟒
= 1/3 × 3.14 × 4
= 12.56/3 cm2
= 4.19 cm2
Area of major sector = ((𝟑𝟔𝟎 − 𝛉))/𝟑𝟔𝟎×𝝅𝒓𝟐
= ((360 − 30))/360 × 3.14 × (4)2
= 𝟑𝟑𝟎/𝟑𝟔𝟎 × 𝟑.𝟏𝟒 × 𝟒 × 𝟒
= 11/12 × 3.14 × 4 × 4
= 46.05 cm2
Example 1 (Method 2)
Find the area of the sector of a circle with radius 4 cm and of angle 30°. Also, find the area of the corresponding major sector (Use π= 3.14).
Given
Radius = r = 4 cm, θ=30°
Now,
Area of sector = 𝜽/𝟑𝟔𝟎 × 𝝅𝒓𝟐
= 30/360 × 3.14 × (4)2
= 𝟏/𝟏𝟐 × 𝟑.𝟏𝟒 × 𝟒 × 𝟒
= 1/3 × 3.14 × 4
= 12.56/3 cm2
= 4.19 cm2
Now,
Area of major sector
= Area of circle – Area of minor sector
Area of circle = 𝜋𝑟2
= 3.14 × 42
= 3.14 × 16
= 50.24 cm2
Now,
Area of major sector
= Area of circle – Area of minor sector
= 50.24 – 4.19
= 46.05 cm2

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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