Example 1 - Chapter 11 Class 10 Areas related to Circles

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