πr²

Chapter 11 · Class X Mathematics · MCQ Practice

MCQ Practice Arena

Areas Related to Circles

Sector, Segment, Composite — Apply the Right Formula Every Time

📋 50 MCQs ⭐ 26 PYQs ⏱ 70 sec/Q

🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs

18Easy

22Medium

10Hard

26PYQs

70 secAvg Time/Q

7Topics

Easy 36% Medium 44% Hard 20%

Why Practise These MCQs?

CBSE Class XState BoardsNTSE

Areas Related to Circles MCQs are formula-substitution heavy — the challenge is picking the RIGHT formula quickly and handling composite figures (circle minus triangle, sector plus rectangle). CBSE Boards assign 6–8 marks annually; composite figure problems are the standard 4-mark format. NTSE includes creative shaded-region problems. Always draw the figure.

Topic-wise MCQ Breakdown

Area & Circumference of Circle6 Q

Area of Sector (θ/360 × πr²)12 Q

Length of Arc8 Q

Area of Minor Segment10 Q

Area of Major Segment3 Q

Annulus (Ring) Area4 Q

Composite Figures (Circle + Polygon)7 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$\text{Area of circle} = \pi r^2$

$\text{Circumference} = 2\pi r$

$\text{Sector area} = \tfrac{\theta}{360}\pi r^2$

$\text{Arc length} = \tfrac{\theta}{360} \times 2\pi r$

$\text{Minor segment} = \text{Sector} - \triangle \text{area}$

$\text{Annulus} = \pi(R^2 - r^2)$

MCQ Solving Strategy

Sector area formula: θ/360 × πr² — the fraction of the full circle. Minor segment = Sector − Triangle — always compute the triangle area using (1/2)r² sinθ for the standard angles (30°, 60°, 90°, 120°). For composite figure MCQs, shade the required region on your diagram and identify whether to ADD or SUBTRACT each component. Use π = 22/7 when radius is a multiple of 7; use π = 3.14 otherwise.

⚠ Common Traps & Errors

⚠Sector area needs θ in DEGREES — if radians are given, convert first
⚠Segment = Sector − Triangle (not Sector − chord)
⚠Major segment = Circle area − Minor segment
⚠Arc length gives PERIMETER of sector, not area
⚠Annulus: subtract areas — π(R²−r²) not π(R−r)²

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Area and circumference, sector area for standard angles

② Medium

Arc length, minor segment, annulus problems

③ Hard

Composite figures with multiple shapes, shaded region

★ PYQ

CBSE — sector + triangle composite; NTSE — elegant shaded areas

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 📘✔️ Exercises Step-by-step NCERT solutions ✔️❌ True / False Concept-based True & False ➡ Next Chapter Surface Areas & Volumes

🎯 Knowledge Check

Maths — AREAS RELATED TO CIRCLES

50 Questions Class 10 MCQs

The formula for the area of a circle of radius $r$ is

a a. $2\pi r$ b b. $\pi r^2$ c c. $\pi d$ d d. $\frac{1}{2}\pi r^2$

If the radius of a circle is doubled, its area becomes

a a. double b b. triple c c. four times d d. eight times

The value of $\pi$ generally used in NCERT problems is

a a. 3 b b. $\frac{21}{7}$ c c. $\frac{22}{7}$ d d. 3.5

A sector of a circle is bounded by

a a. two chords b b. two tangents c c. two radii and an arc d d. a chord and an arc

The total angle at the centre of a circle is

a a. $90^\circ$ b b. $180^\circ$ c c. $270^\circ$ d d. $360^\circ$

The area of a sector of angle $\theta^\circ$ and radius $r$ is

a a. $\theta \pi r^2$ b b. $\frac{360}{\theta}\pi r^2$ c c. $\frac{\theta}{360}\pi r^2$ d d. $\frac{\theta}{180}\pi r^2$

A sector whose angle is less than $180^\circ$ is called

a a. major sector b b. minor sector c c. segment d d. arc

A sector whose angle is more than $180^\circ$ is called

a a. minor sector b b. semicircle c c. major sector d d. segment

A segment of a circle is bounded by

a a. two radii b b. a radius and an arc c c. a chord and an arc d d. two chords

The smaller region formed by a chord and an arc is called

a a. major segment b b. minor segment c c. sector d d. semicircle

The area of a minor segment is found by

a a. adding triangle area to sector area b b. subtracting triangle area from sector area c c. subtracting sector area from circle area d d. adding sector area to circle area

The area of a major segment is

a a. area of circle - area of major sector b b. area of sector - area of triangle c c. area of circle - area of minor segment d d. area of triangle - area of sector

Which of the following is a chord of a circle?

a a. Diameter b b. Radius c c. Tangent d d. Arc

The longest chord of a circle is

a a. radius b b. tangent c c. diameter d d. arc

If the diameter of a circle is $14$ cm, its radius is

a a. 14 cm b b. 28 cm c c. 7 cm d d. 21 cm

The area of a semicircle of radius $r$ is

a a. $\pi r^2$ b b. $\frac{1}{2}\pi r^2$ c c. $2\pi r^2$ d d. $\pi r$

The unit of area related to circles is

a a. cm b b. cm$^3$ c c. cm$^2$ d d. m

If the radius of a circle is zero, its area is

a a. $\pi$ b b. 1 c c. 0 d d. undefined

A quadrant of a circle subtends an angle of

a a. $45^\circ$ b b. $60^\circ$ c c. $90^\circ$ d d. $180^\circ$

The area of a quadrant of radius $r$ is

a a. $\pi r^2$ b b. $\frac{1}{2}\pi r^2$ c c. $\frac{1}{4}\pi r^2$ d d. $2\pi r^2$

Which concept is most useful in finding shaded regions?

a a. Volume b b. Area subtraction c c. Linear equations d d. Probability

The boundary length of a circle is called

a a. area b b. diameter c c. circumference d d. radius

The formula for circumference of a circle is

a a. $\pi r^2$ b b. $2\pi r$ c c. $\pi d^2$ d d. $\frac{1}{2}\pi r$

The area of a sector is directly proportional to

a a. radius b b. diameter c c. central angle d d. circumference

A circle is divided into equal sectors. The areas of the sectors are

a a. unequal b b. proportional to radius c c. equal d d. zero

The region enclosed between two concentric circles is called

a a. sector b b. segment c c. ring d d. arc

The area of a ring depends on

a a. inner radius only b b. outer radius only c c. difference of radii d d. difference of squares of radii

In exams, shaded region problems mostly involve

a a. only triangles b b. only rectangles c c. only circles d d. combination of figures

Which value of $\pi$ is used when radius is a multiple of 7?

a a. 3 b b. $\frac{22}{7}$ c c. 3.14 d d. 2.17

The area of a sector with angle $180^\circ$ is

a a. full circle b b. half circle c c. one-third circle d d. quadrant

Which figure is formed by a diameter and an arc?

a a. sector b b. semicircle c c. segment d d. quadrant

The area of a minor segment is always

a a. greater than half the circle b b. equal to half the circle c c. less than half the circle d d. equal to the triangle area

To find the area of a major sector, we usually

a a. add triangle area b b. subtract minor sector from circle c c. subtract triangle from sector d d. add all parts

Which mathematical idea links angles and areas in circles?

a a. Linear equations b b. Proportionality c c. Probability d d. Statistics

A wheel of radius $r$ completes one full rotation. The area covered relates to

a a. circumference b b. diameter c c. area of circle d d. area of square

The region enclosed by a chord and the major arc is

a a. minor segment b b. major segment c c. sector d d. semicircle

Which topic is essential before studying this chapter?

a a. Trigonometry b b. Circles basics c c. Probability d d. Statistics

Area related to circles belongs to which branch of mathematics?

a a. Algebra b b. Geometry c c. Arithmetic d d. Calculus

If the radius is given in metres, the area will be in

a a. m b b. m$^2$ c c. cm$^2$ d d. km

Which of the following is NOT a part of this chapter?

a a. Area of sector b b. Area of segment c c. Surface area of sphere d d. Area of circle

The area of a circle increases when

a a. radius decreases b b. radius increases c c. diameter is zero d d. centre changes

A semicircle subtends an angle of

a a. $90^\circ$ b b. $120^\circ$ c c. $180^\circ$ d d. $360^\circ$

The formula $\frac{\theta}{360}\times \pi r^2$ is based on

a a. addition b b. subtraction c c. ratio d d. multiplication only

In shaded region problems, the first step should be

a a. substitute values b b. write the answer c c. identify required region d d. choose value of $\pi$

Which shape helps in finding segment area?

a a. rectangle b b. square c c. triangle d d. trapezium

The area of a circle is zero when

a a. diameter is maximum b b. radius is negative c c. radius is zero d d. $\pi=0$

Which figure gives maximum area for a fixed perimeter?

a a. square b b. rectangle c c. circle d d. triangle

The formula for area of a ring is

a a. $\pi(R+r)^2$ b b. $\pi(R^2-r^2)$ c c. $2\pi(R-r)$ d d. $\pi(R-r)^2$

Which problems are most common in board exams from this chapter?

a a. Proofs only b b. Constructions only c c. Numerical problems d d. Graphs only

This chapter mainly strengthens which skill?

a a. Memorisation b b. Drawing c c. Logical application of formulas d d. Speed writing

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Areas Related To Circles | Mathematics Class 10 | Academia Aeternum — Complete Notes & Solutions · academia-aeternum.com

These multiple-choice questions are carefully designed to provide conceptual clarity, formula mastery, and exam-oriented practice for NCERT Class X Mathematics Chapter 11, Areas Related to Circles. The MCQs systematically cover every essential aspect of the chapter, including the area of a circle, sectors, segments, major and minor regions, shaded areas, proportionality of angles and areas, and real-life applications. Each question follows the NCERT framework and mirrors the latest CBSE…

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Frequently Asked Questions

A circle is the locus of all points in a plane that are at a fixed distance, called the radius, from a fixed point known as the centre.

The area of a circle is the region enclosed by its circumference and is calculated using the formula $A = \pi r^2$.

$\pi$ is a constant representing the ratio of the circumference of a circle to its diameter, commonly taken as $\frac{22}{7}$ or 3.14.

A sector is the region bounded by two radii and the arc between them.

A minor sector is the smaller sector formed when the central angle is less than $180^\circ$.

A major sector is the larger sector formed when the central angle is greater than $180^\circ$.

The area of a sector is $\frac{\theta}{360^\circ} \times \pi r^2$, where $\theta$ is the central angle.

The angle at the centre determines what fraction of the circle the sector occupies, directly affecting its area.

A segment is the region bounded by a chord of a circle and the corresponding arc.

A minor segment is the smaller region formed between a chord and the corresponding minor arc.

A major segment is the larger region formed between a chord and the corresponding major arc.

Area of minor segment = Area of corresponding sector - Area of the triangle formed by the radii and chord.

Area of major segment = Area of the circle - Area of the minor segment.

A triangle helps remove the straight-line portion inside the sector, leaving only the curved region of the segment.

A chord is a line segment joining any two points on the circumference of a circle.

AREAS RELATED TO CIRCLES – Learning Resources

Detailed Notes

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NCERT Solutions

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Areas Related to Circles

MCQ Bank Snapshot

Why Practise These MCQs?

Topic-wise MCQ Breakdown

Must-Know Formulae Before You Start

MCQ Solving Strategy

⚠ Common Traps & Errors

Difficulty Ladder

Continue Your Preparation

Maths — AREAS RELATED TO CIRCLES

Frequently Asked Questions

Q 01 What is meant by a circle in geometry?

Q 02 What is the area of a circle?

Q 03 What does \(\pi\) represent in circle formulas?

Q 04 Define a sector of a circle.

Q 05 What is a minor sector?

Q 06 What is a major sector?

Q 07 How is the area of a sector calculated?

Q 08 Why is the angle at the centre important in sector problems?

Q 09 What is a segment of a circle?

Q 10 What is a minor segment?

Q 11 What is a major segment?

Q 12 How do you find the area of a minor segment?

Q 13 How is the area of a major segment obtained?

Q 14 Why are triangles used while finding the area of a segment?

Q 15 What is a chord of a circle?

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AREAS RELATED TO CIRCLES – Learning Resources

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NCERT Solutions

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