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

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Exercise 1

Exercise 2 (Part 2)

Exercise 3 (Part 1)

Exercise 3 (Part 2)