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Class 10 Areas Related to Circles: 8 practice questions with answers, step by step
These are 8 practice questions on NCERT Class 10 Maths Chapter 11, Areas Related to Circles, each with a worked answer and the units. They cover the area of a circle, the area of a sector, the length of an arc, a quadrant, and the area of a segment. Use π = 22/7 in every question. Try each one on paper before you open the answer. The tangents chapter has its own set: the Class 10 Circles questions.
These questions are our own, drafted with AI help. Every answer was re-computed by a test script, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.
What the chapter says you need
Facts from the NCERT textbook (Mathematics, Textbook for Class X, Reprint 2026-27, Chapter 11, printed pages 154 to 160):
- A sector is the part of a circular region enclosed by two radii and the corresponding arc; a segment is the part enclosed by a chord and the arc. The smaller one is the minor segment or minor sector, and the textbook's "segment" and "sector" mean the minor ones unless stated otherwise (section 11.1, page 154).
- The area of a circle is πr²; a circle can be thought of as a sector of angle 360° (page 155).
- Area of a sector of angle θ (in degrees) = (θ/360) × πr², and length of an arc of a sector of angle θ = (θ/360) × 2πr (page 155; summary, page 160).
- Area of a segment = area of the sector − area of the triangle formed by the two radii and the chord (page 156; summary, page 160).
Circle, sector and arc
Question 1. Find the area of a circle of radius 21 cm, taking π = 22/7, in square cm.
Answer: 1,386 cm². Area = πr² = 22/7 × 21 × 21 = 22 × 3 × 21 = 1,386 cm².
Question 2. Find the area of a sector of radius 14 cm and angle 90°, taking π = 22/7, in square cm.
Answer: 154 cm². Area = (90/360) × πr² = 1/4 × 22/7 × 14 × 14 = 1/4 × 616 = 154 cm².
Question 3. Find the length of the arc of a sector with radius 21 cm and angle 60°, taking π = 22/7, in cm.
Answer: 22 cm. Arc = (60/360) × 2πr = 1/6 × 2 × 22/7 × 21 = 1/6 × 132 = 22 cm.
Question 4. A quadrant (a quarter of a circle) has a radius of 28 cm. Taking π = 22/7, what is its area in square cm?
Answer: 616 cm². A quadrant is a sector of angle 90°, so its area = 1/4 × πr² = 1/4 × 22/7 × 28 × 28 = 1/4 × 2,464 = 616 cm².
Segments and applications
Question 5. A chord of a circle of radius 14 cm makes a right angle at the centre. Taking π = 22/7, what is the area of the minor segment in square cm?
Answer: 56 cm². Segment = sector − triangle (page 156). Sector = 90/360 × 22/7 × 14 × 14 = 154 cm². The triangle has two sides of 14 cm at right angles, so its area = 1/2 × 14 × 14 = 98 cm². Segment = 154 − 98 = 56 cm².
Question 6. Find the area of a sector of radius 7 cm and angle 60°, taking π = 22/7, in square cm to two decimal places.
Answer: about 25.67 cm². Area = (60/360) × 22/7 × 7 × 7 = 1/6 × 154 = 77/3 ≈ 25.67 cm².
Question 7. An arc of a circle of radius 21 cm is 11 cm long. What angle does it make at the centre, in degrees, taking π = 22/7?
Answer: 30°. Arc length = (θ/360) × 2πr, and 2πr = 2 × 22/7 × 21 = 132 cm. So 11 = (θ/360) × 132, giving θ = 11 × 360 ÷ 132 = 30°.
Question 8. The minute hand of a clock is 14 cm long. How far does the tip of the hand move in 20 minutes, taking π = 22/7, in cm to two decimal places?
Answer: about 29.33 cm. The minute hand turns 360° in 60 minutes, so in 20 minutes it turns 120°. The tip moves along an arc: (120/360) × 2 × 22/7 × 14 = 1/3 × 88 = 88/3 ≈ 29.33 cm.
Practise more, and check your marks
- Free practice, marked instantly in your browser: Class 10 Areas Related to Circles questions. Questions 1 to 5 above are all in this set.
- Printable worksheets with answer keys, in English, Hindi and Marathi: Class 10 worksheets.
- See which unit this chapter belongs to and how CBSE splits the 80 theory marks in our Class 10 Maths syllabus 2026-27 guide.
- The same step-by-step style for neighbouring chapters: Class 10 Surface Areas and Volumes and Class 10 Triangles.
Where CMDLearn fits
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Sources
All opened and read on 21 October 2026. Page numbers are the printed page numbers of the textbook.
- NCERT, Mathematics, Textbook for Class X, Chapter 11 "Areas Related to Circles" (Reprint 2026-27), printed pages 154-160 (sector and segment, section 11.1, page 154; the area of a sector and the length of an arc, page 155; the area of a segment, page 156; summary, page 160): ncert.nic.in/textbook/pdf/jemh111.pdf
The formulas are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the official CBSE notices.