Class 10 Mathematics
Area of Circle
Exercise 12.2 (NCERT) Part 1
Question 1: Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.
Solution: Area of sector
Question 2: Find the area of a quadrant of a circle whose circumference is 22 cm.
Solution: Radius can be calculated as follows:
Area of quadrant can be calculated as follows:
Question 3: The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.
Solution: The minute hand makes an angle of 360o in 60 minutes.
Hence, angle made in 5 minutes = 30o
Area of sector
Question 4: A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding: (i) minor segment (ii) major sector.
Solution:Area of minor sector
Area of major sector
Area of triangle formed by two radii
Area of minor segment = Area of minor sector – area of triangle
= 25π - 50 = 25(π - 2)
= 25(3.14 – 2) = 25 x 1.14 = 28.5 sq cm
Question 5: In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find:
- the length of the arc
- area of the sector formed by the arc
- area of the segment formed by the corresponding chord
Solution: Length of Arc can be calculated as follows:
Area of corresponding sector can be calculated as follows:
As the angle made by radii is 60o, so this is an equilateral triangle; because angles opposite to both radii will be equal.
Area of equilateral triangle can be calculated as follows:
Question 6: A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle.
Solution: Let us use previous figure to find area of triangle
Area of circle = πr2 = π152 = 225π = 706.5 sq cm
Area of minor sector
Area of minor segment = 117.75 – 97.425 =20.325 sq cm
Area of major segment = 706.5 – 20.325 = 686.175 sq cm
Exercise 2 (Part 2)
Exercise 3 (Part 1)
Exercise 3 (Part 2)