Areas Related to Circles — Previous Year Questions (Class 10 Mathematics)
Calculating areas of circles, sectors, and segments is essential in geometry. These concepts are applied in real-world problems involving land measurement
TL;DR: Calculating areas of circles, sectors, and segments is essential in geometry. These concepts are applied in real-world problems involving land measure…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
Calculating areas of circles, sectors, and segments is essential in geometry. These concepts are applied in real-world problems involving land measurement
Areas Related to Circles — Previous Year Questions with Solutions
Q (2023, 2 marks): Find the area of a sector of a circle with radius 7 cm and central angle 60°.
Answer: Area of sector = (θ / 360°) × π × r^2
= (60° / 360°) × π × 7^2
= (1/6) × π × 49
= 49π / 6 cm^2
= (49 × 22) / (6 × 7) cm^2
= 1078 / 42 cm^2
≈ 25.67 cm^2
Q (2022, 3 marks): A circle has radius 10 cm. Find the area of the segment corresponding to a chord that subtends an angle of 90° at the center.
Answer: Area of sector = (90° / 360°) × π × 10^2 = (1/4) × 100π = 25π cm^2
Area of triangle AOB = (1/2) × 10 × 10 × sin(90°) = (1/2) × 100 × 1 = 50 cm^2
Area of segment = Area of sector - Area of triangle
= 25π - 50
= 25(π - 2) cm^2
≈ 28.54 cm^2
Q (2023, 2 marks): Find the length of the arc of a sector with radius 14 cm and central angle 45°.
Answer: Length of arc = (θ / 360°) × 2π × r
= (45° / 360°) × 2π × 14
= (1/8) × 2 × 22/7 × 14
= (1/8) × 2 × 22 × 2
= (1/8) × 88
= 11 cm
Q (2022, 3 marks): A circular park has radius 21 m. A path of width 7 m runs around it. Find the area of the path.
Answer: Radius of inner circle = 21 m
Radius of outer circle = 21 + 7 = 28 m
Area of outer circle = π × 28^2 = 784π m^2
Area of inner circle = π × 21^2 = 441π m^2
Area of path = 784π - 441π = 343π m^2
= 343 × 22/7 m^2
= 343 × 22 / 7 m^2
= 1078 m^2
Q (2023, 2 marks): Find the area of a circle that has circumference 88 cm.
Answer: Circumference = 2πr = 88
2 × (22/7) × r = 88
(44/7) × r = 88
r = 88 × 7 / 44 = 14 cm
Area = πr^2 = (22/7) × 14^2 = (22/7) × 196 = 22 × 28 = 616 cm^2
Q (2021, 2 marks): Two concentric circles have radii 8 cm and 5 cm. Find the area of the ring (annulus) between them.
Answer: Area of outer circle = π × 8^2 = 64π cm^2
Area of inner circle = π × 5^2 = 25π cm^2
Area of ring = 64π - 25π = 39π cm^2
= 39 × 22/7 cm^2
= 858/7 cm^2
≈ 122.57 cm^2
Frequently Asked Questions
What is the formula for the area of a sector and how is it derived?
The area of a sector is (θ / 360°) × πr^2, where θ is the central angle in degrees. This is derived from the fact that a sector is a proportional part of the full circle, and the area is proportional to the angle subtended.
What is the difference between a segment and a sector of a circle?
A sector is the region bounded by two radii and an arc. A segment is the region bounded by a chord and the arc it cuts off. The segment's area equals the sector's area minus the triangle formed by the two radii and the chord.
More Class 10 Mathematics PYQs
🤖 Stuck on any of these? Ask Syllab's free AI Tutor to explain step by step →