Maths · Mensuration · chapter 11 of 14

Class 10 Maths Chapter 11: Areas Related to Circles MCQs with answers

10 multiple-choice questions on Areas Related to Circles, each with its answer and the reason, written from the NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.

Question 1
A round cake of radius 14 cm is cut into four equal pieces along two perpendicular diameters. The area of the top of one piece is. Take π = 22/7.
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Answer: (a) 154 cm²

Each piece is a sector of angle 90°: (90/360) × (22/7) × 14² = 154 cm². 616 cm² is the whole top, 22 cm² is the arc length taken as an area, 308 cm² is half the cake.

Question 2
A curved garden path follows an arc of a circle of radius 42 m, and the arc subtends 120° at the centre. The length of the path is. Take π = 22/7.
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Answer: (d) 88 m

Arc = (120/360) × 2 × (22/7) × 42 = 88 m. 44 m drops the 2 of 2πr, 176 m doubles the arc, 1848 is the sector's area.

Question 3
Two radii of a circle make an angle of 120° at the centre. The angle of the major sector they form is
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Answer: (b) 240°

The major sector's angle is 360° − 120° = 240°. 60° is 180° − 120°, as if the angles made a straight line.

Question 4
The part of a circular region enclosed between a chord and the arc it cuts off is called
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Answer: (c) a segment

A chord and its arc enclose a segment. A sector is bounded by two radii and an arc, a quadrant is a 90° sector, and an arc is a curve, not a region.

Question 5
A chord PQ divides a circular disc into two unequal parts. When a question says only 'the segment PQ', it means
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Answer: (a) the minor segment

Unless stated otherwise, 'segment' means the minor segment.

Question 6
Two radii of a circle of radius 28 cm are perpendicular. The area of the major sector they form is. Take π = 22/7.
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Answer: (d) 1848 cm²

Circle = (22/7) × 28² = 2464 cm²; minor sector = 2464/4 = 616 cm²; major sector = 2464 − 616 = 1848 cm².

Question 7
OA and OB are radii of a circle of radius 12 cm with ∠AOB = 90°. The area of triangle OAB is
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Answer: (a) 72 cm²

The triangle is right-angled at O with legs 12 cm and 12 cm: ½ × 12 × 12 = 72 cm². 144 forgets the ½; 36√3 is the 60° (equilateral) formula.

Question 8
OA and OB are radii of a circle of radius 10 cm with ∠AOB = 60°. The area of triangle OAB is
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Answer: (d) 25√3 cm²

With a 60° angle between equal sides the triangle is equilateral of side 10 cm: (√3/4) × 10² = 25√3 cm². 50 cm² treats it as right-angled.

Question 9
A circular mirror with centre O and radius 28 cm has a strip cut off along a straight line AB, where ∠AOB = 60°. The area of the strip cut off is. Take π = 22/7.
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Answer: (b) (12323 − 196√3) cm²

Sector = (60/360) × (22/7) × 28² = 1232/3 cm²; triangle (equilateral, side 28) = (√3/4) × 784 = 196√3 cm²; segment = sector − triangle.

Question 10
The angle of a sector is kept the same and its radius is doubled. Then
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Answer: (b) its arc length doubles and its area becomes four times

Arc = (θ/360) × 2πr grows as r, so it doubles; area = (θ/360) × πr² grows as r², so it becomes 2² = 4 times.

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