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NCERT Solutions for Class 10 Maths Chapter 11 Areas Related to Circles

NCERT Solutions for Class 10 Maths Chapter 11 Areas Related to Circles covers the perimeter and area of a circle, and the areas of sectors and segments of a circle, along with combinations of plane figures.

Overview of Topics & Subtopics (Click to Jump)

1. Perimeter and Area of a Circle — A Review

Short Note:

• Circumference of a circle of radius r = 2πr. Area of a circle of radius r = πr².

2. Areas of Sector and Segment of a Circle

Short Note:

• Area of a Sector with angle θ (in degrees) at the centre = (θ/360°) × πr².

• Length of an Arc = (θ/360°) × 2πr.

• Area of a Segment = Area of the corresponding sector − Area of the triangle formed by the two radii and the chord.

3. Areas of Combinations of Plane Figures

Short Note:

• Areas of combined or composite figures (such as a square with circles/semicircles cut out or added) are found by adding or subtracting the areas of the basic shapes (circle, square, rectangle, triangle, sector) that make up the figure.

NCERT Textbook Exercise Questions

Find the area of a sector of a circle with radius 6 cm, if the angle of the sector is 60°.
Answer: Area = (60/360) × π × 6² = (1/6) × 22/7 × 36 = 132/7 ≈ 18.86 cm².
Find the area of a quadrant of a circle whose circumference is 22 cm.
Answer: 2πr = 22 ⇒ r = 22/(2×22/7) = 3.5 cm. Area of quadrant = ¼πr² = ¼ × 22/7 × 3.5² = 9.625 cm².
Find the area of the sector of a circle with radius 4 cm and angle 30°. Also find the area of the corresponding major sector.
Answer: Minor sector area = (30/360) × π × 4² = (1/12) × 22/7 × 16 = 176/84 ≈ 4.19 cm². Total circle area = πr² = 22/7 × 16 ≈ 50.29 cm². Major sector area = 50.29 − 4.19 ≈ 46.1 cm².
A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding minor segment.
Answer: Sector area (90°) = (90/360) × π × 10² = ¼ × 22/7 × 100 ≈ 78.57 cm². Triangle area = ½ × 10 × 10 = 50 cm². Segment area = 78.57 − 50 = 28.57 cm².
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Class 10 › Mathematics › Areas Related to Circles
Chapter notesRead the chapterPractice MCQsCheck what you rememberChapter test10 questions on one pageOnline testTest 1, 2 and 3, one question at a timePYQPrevious year questionsStudy materialPDF notes
Topics in this chapter: Perimeter and Area of a Circle — A ReviewAreas of Sector and Segment of a CircleAreas of Combinations of Plane Figures