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Areas Related to Circles — Class 10 MCQs with Answers

Class 10 CBSE Mathematics · Chapter 11

108 practice questions · 31 Easy · 39 Medium · 38 Hard · Updated

Jump to the 6 solved questions

Practise the most important Class 10 CBSE Mathematics questions from Chapter 11, "Areas Related to Circles". You get 11 timed quizzes made from 108 NCERT-based MCQs, with answers and explanations. The questions are split into 31 Easy, 39 Medium and 38 Hard. Warm up on the basics, then move on to the exam-level questions that top scorers in CBSE Board exams and the JEE & NEET foundation years get right.

To score well in "Areas Related to Circles", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This helps you stay accurate when time is short, just as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.

Use this chapter for focused revision. Start with the Easy set to check your basics on Areas Related to Circles, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 10 Mathematics mastery score. Try the 6 sample questions below: tap an option to see the answer and a worked explanation. Sign in free to start practising.

Areas Related to Circles — important questions & MCQs with answers (Class 10 Mathematics)

6 solved questions from this chapter's difficulty levels, each with its answer and explanation. Tap an option to check yourself.

0 of 6 answered

  1. Q1 of 6Easy

    Circumference of a circle of radius r:

    Show answer

    Answer: 2πr

    Explanation: Circumference = 2πr, the perimeter formula for a circle — don't confuse it with area = πr², which grows with r² not r.

  2. Q2 of 6Easy

    Area of a circle of radius r is:

    Show answer

    Answer: πr²

    Explanation: Area = πr² — the radius is squared, unlike circumference (2πr) which is linear in r, a common mix-up between the two formulas.

  3. Q3 of 6Medium

    Area of a sector of radius 7 cm and angle 90° (π = 22/7):

    A circle with centre O; a sector of radius 7 cm with a right angle at the centre is shaded.

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    Answer: 38.5 cm²

    Explanation: Sector area = (θ/360) × πr² = (90/360) × (22/7×49) = (1/4)×154 = 38.5 cm² — a quarter of the full circle's area since 90° is a quarter turn.

  4. Q4 of 6Medium

    Assertion (A): In a circle of radius 21 cm, the arc that subtends an angle of 60° at the centre is 22 cm long. (Use π = 22/7.) Reason (R): The length of an arc of a sector of angle θ is (θ/360) × πr².

    Show answer

    Answer: A is true but R is false

    Explanation: A is true: arc length = (60/360) × 2 × (22/7) × 21 = 22 cm. R is false: the arc length is (θ/360) × 2πr; (θ/360) × πr² is the area of the sector.

  5. Q5 of 6Hard

    A wheel rotates 1000 times in 5 minutes to cover a distance. If diameter = 70 cm, distance covered (km, π = 22/7):

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    Answer: 2.2 km

    Explanation: Circumference = πd = (22/7)×70 = 220 cm per revolution; 1000 revolutions = 220,000 cm = 2200 m = 2.2 km.

  6. Q6 of 6Hard

    Assertion (A): A chord of a circle of radius 10 cm subtends a right angle at the centre. The area of the minor segment is 28.5 cm². (Use π = 3.14.) Reason (R): Area of a segment = area of the corresponding sector − area of the corresponding triangle.

    Show answer

    Answer: Both A and R are true and R is the correct explanation of A

    Explanation: Both are true. Sector area = (90/360) × 3.14 × 100 = 78.5 cm² and triangle area = ½ × 10 × 10 = 50 cm², so the segment is 28.5 cm². R is the rule that gives A, so it explains A.

Areas Related to Circles notes: key concepts (Class 10 Mathematics)

This chapter measures parts of a circle: the whole area and circumference, the slice cut by two radii, and the region cut off by a chord. Combining these with squares and triangles handles the composite shaded-region figures that boards favour.

Circumference of a circle
The distance around the circle, 2πr — a length, not an area, and measured in ordinary units.
Area of a circle
The space enclosed, πr², measured in square units. Confusing it with circumference is the classic error.
Sector of a circle
The region bounded by two radii and the arc between them, like a slice of pie.
A circle with centre O. Two radii OA and OB, each r, make an angle θ at the centre. The smaller slice between them, shaded green, is the minor sector, bounded by the two radii and the arc AB (drawn thick). The rest of the circle, shaded amber, is the major sector, with angle 360° − θ. Below: arc length = (θ/360) × 2πr and area of sector = (θ/360) × πr².
Angle of a sector
The angle θ at the centre, which fixes what fraction θ/360 of the whole circle the sector represents.
Length of an arc
The fraction θ/360 of the full circumference, giving the curved boundary of the sector.
Area of a sector
The fraction θ/360 of the circle's total area, so a 90° sector is exactly a quarter of the circle.
Perimeter of a sector
The arc length PLUS the two radii — the straight edges must be included, which is easy to forget.
Segment of a circle
The region between a chord and its arc, found by subtracting the triangle's area from the sector's area.
A circle with centre O, drawn dashed. Radii OA and OB are drawn, and the chord AB joins their ends. The triangle OAB is shaded blue. The region between the chord AB and the arc AB, shaded amber, is the segment. Below: area of segment = area of sector OAB − area of triangle OAB.
Minor and major parts
The smaller sector or segment is minor and the larger is major; the two together make the whole circle.
Area of a ring (annulus)
The region between two concentric circles, equal to π(R² − r²).
Two circles with the same centre O. The ring between them is shaded green. The outer radius is drawn to the right and marked R; the inner radius is drawn down-left and marked r. Below: area of ring = πR² − πr² = π(R² − r²).
Combination and shaded regions
Composite figures are handled by adding the areas of known shapes or subtracting a removed piece from a surrounding one.
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Areas Related to Circles — FAQs

What are the key concepts in Class 10 Mathematics Areas Related to Circles?+

This chapter measures parts of a circle: the whole area and circumference, the slice cut by two radii, and the region cut off by a chord. Combining these with squares and triangles handles the composite shaded-region figures that boards favour. Key ideas include Circumference of a circle, Area of a circle, Sector of a circle, Angle of a sector, Length of an arc, Area of a sector.

What does Class 10 Mathematics Chapter 11 (Areas Related to Circles) cover on XamBaaz?+

It has 108 NCERT-based MCQs on "Areas Related to Circles": 31 Easy, 39 Medium and 38 Hard. Together they make 11 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams and the JEE & NEET foundation years.

Are these "Areas Related to Circles" questions free to practise?+

Yes. Sign in with Google to practise "Areas Related to Circles" free. Full unlimited access is ₹999/year. One year from the day you pay. You stay in Class 10 till 31 March; on 1 April your account moves up to Class 11 and the rest of your year carries over. No chapter is charged separately.

How should I revise "Areas Related to Circles" for the exam?+

Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 11 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.

Are these "Areas Related to Circles" MCQs available with answers?+

Yes. 6 sample questions are on this page with answers: tap an option, or "Show answer", to see the correct option and a step-by-step explanation. Sign in free with Google to start practising, with instant scoring.

Is there negative marking in the "Areas Related to Circles" quizzes?+

Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.

What are the important questions from Areas Related to Circles (Class 10 Mathematics)?+

The questions that matter most test Circumference of a circle, Area of a circle, Sector of a circle, Angle of a sector, Length of an arc, Area of a sector. This page shows 6 solved important MCQs with answers and explanations. Sign in to practise all 108 questions on the chapter as timed quizzes.

Is there an online quiz for Areas Related to Circles?+

Yes — Class 10 Mathematics Areas Related to Circles has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.

Are there question answers and extra questions for Areas Related to Circles (Class 10 Mathematics)?+

Yes. This page has 6 solved questions on Areas Related to Circles, each with the correct answer and a short explanation. Sign in to practise all 108 questions on the chapter as timed quizzes.

Are there assertion–reason and case study questions for Areas Related to Circles (Class 10 Mathematics)?+

Yes. The Areas Related to Circles question bank has 6 assertion–reason questions and 12 case-based (case study) questions in the CBSE board format, alongside the regular MCQs. Each comes with the answer and a worked explanation. Sign in to practise them in timed quizzes.

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