NCERT Class 10 Maths — Chapter 11

Exercise 11.2: Area of Sector and Segment

Find the area of sectors (pizza slices) and segments (the region between a chord and an arc). Most board questions come from this exercise.

sector areaarc lengthsegment areaminor and major sector
14
NCERT Questions
10
Practice MCQs
4
Key Concepts
Free
With Answers

Extra Practice Questions

These questions cover the same concepts as Exercise 11.2. Try solving them to build confidence before or after the textbook exercise.

1

Ravi wants to find the length of the arc of a sector with radius 7 cm and angle 90°. He applies the formula: Arc Length = (90/360) × π(7)². What mistake did Ravi make?

A.He used the wrong value for π.
B.He used the formula for the area of a sector instead of arc length.
C.He used the incorrect angle in the formula.
D.He squared the radius when it should be multiplied by 2.
2

A clock's minute hand is 10 cm long. How far does the tip of the minute hand move in 30 minutes? (Use π = 3.14)

A.15.7 cm
B.31.4 cm
C.62.8 cm
D.10 cm
3

A circle C1 is inscribed in an equilateral triangle of side 'a'. Another circle C2 is circumscribed about the same equilateral triangle. Find the ratio of the area of C1 to the area of C2.

A.1:2
B.1:3
C.1:4
D.1:9
4

Two circles of the same radius 'r' intersect each other such that each passes through the center of the other. Find the area of the common region (lens).

A.(π/2 - √3/4)r²
B.(2π/3 - √3/2)r²
C.(π/3 - √3/4)r²
D.(π/3 - √3/2)r²
5

A square ABCD has side length 'a'. Four semi-circles are drawn *outwards* with each side of the square as diameter. Find the perimeter of the entire figure formed.

A.πa
B.2πa
C.πa/2
D.(π + 2)a
6

Which of the following statements is TRUE regarding a sector of a circle with radius 'r' and central angle 'θ' (in degrees)?

A.The area of the sector is directly proportional to θ, but the length of the arc is proportional to θ².
B.Both the area of the sector and the length of the arc are directly proportional to θ.
C.The area of the sector is proportional to r², but the length of the arc is proportional to r².
D.Neither the area of the sector nor the length of the arc is directly proportional to θ.
7

A chord of a circle of radius 14 cm subtends an angle of 90° at the centre. Find the area of the corresponding major segment. (Use π = 22/7)

A.308 cm²
B.462 cm²
C.518 cm²
D.616 cm²
8

Let ABC be a right-angled triangle with hypotenuse BC. Semi-circles are drawn externally on each side of the triangle as diameters. If the area of the semi-circle on AB is A1, on AC is A2, and on BC is A3, which of the following statements is always true?

A.A1 + A2 = A3
B.A1² + A2² = A3²
C.A1 + A2 > A3
D.A1 + A2 < A3
9

If the perimeter of a semi-circular protractor is 36 cm, then its diameter is: (Use π = 22/7)

A.7 cm
B.10 cm
C.14 cm
D.21 cm
10

If the radius of a sector is increased by 25% and its central angle is decreased by 20%, what is the percentage change in its area?

A.10% increase
B.12.5% increase
C.20% increase
D.25% increase

Stuck on a question?

Paste any question from Exercise 11.2 into our AI Maths Solver and get a step-by-step solution instantly. It works for all NCERT questions.

Try AI Solver — Free

Common Mistakes to Avoid

  • Confusing sector (two radii + arc) with segment (chord + arc)
  • Not converting the angle to use in the formula
  • Forgetting to subtract the triangle area to get the segment area

Other Exercises in Chapter 11

Frequently Asked Questions

What is the formula for area of a sector?

Area of sector = (θ/360°) × πr², where θ is the angle at the centre.

How many questions are in Exercise 11.2?

Exercise 11.2 has 14 questions on sectors, segments, and arc lengths.

Want to practise on paper? Download a free worksheet for this topic.

Download Worksheet PDF