Class 10 Mathematics

Area of Circle

Exercise 12.2 (NCERT Book) 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

10 circle area exercise solution


Question 2: Find the area of a quadrant of a circle whose circumference is 22 cm.

Solution: Radius can be calculated as follows:

10 circle area exercise solution

Area of quadrant can be calculated as follows:

10 circle area exercise solution

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

10 circle area exercise solution

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

10 circle area exercise solution

Area of major sector

10 circle area exercise solution

Area of triangle formed by two radii

10 circle area exercise solution

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:

10 circle area exercise solution

Area of corresponding sector can be calculated as follows:

10 circle area exercise solution
10 circle area exercise solution

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:

10 circle area exercise solution

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

10 circle area exercise solution

Area of circle = πr2 = π152 = 225π = 706.5 sq cm

Area of minor sector

10 circle area exercise solution

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)