Class 10 • Maths • Chapter 11
AREAS RELATED TO CIRCLES
True & False Quiz
Sector. Segment. Combine.
✓True
✗False
25
Questions
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Ch.11
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Why True & False for AREAS RELATED TO CIRCLES?
How this format sharpens your conceptual clarity
🔵 This chapter blends geometry and algebra to find composite areas — a skill directly tested in application problems every year.
✅ T/F distinguishes sector from segment and tests the correct formula for each — a distinction most students confuse.
🎯 Segment area = Sector area − Triangle area; a sector includes the triangle — the segment does NOT.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
The circumference of a circle of radius \(r\) is given by \(2\pi r.\)
Q 2
The area of a circle becomes four times if its radius is doubled.
Q 3
The area of a circle is directly proportional to its radius.
Q 4
The length of an arc of a sector of angle \(\theta\) (in degrees) in a circle of radius \(r\) is \(\dfrac{\theta}{360^\circ} \times 2\pi r\)
Q 5
The area of a sector of angle \(\theta\) (in degrees) in a circle of radius \(r\) is \(\dfrac{\theta}{360^\circ} \times \pi r^2\)
Q 6
A segment of a circle is the region between two radii and the corresponding arc.
Q 7
The area of a segment of a circle is obtained by subtracting the area of the corresponding triangle from the area of the corresponding sector.
Q 8
The area of a ring (or circular path) with outer radius \(R\) and inner radius \(r\) is \(\pi(R^2 - r^2)\)
Q 9
If two circles have equal circumferences, then their areas must be different.
Q 10
If the diameter of a circle is 14 cm, then its radius is 7 cm.
Q 11
The circumference of a circle is numerically equal to the area of the circle for radius \(r=2r\)
Q 12
In the formulae of this chapter, \(\pi\) is often taken as \(\dfrac{22}{7}\) or 3.14 for numerical calculations.
Q 13
The area of a semicircle of radius rrr is \(\pi r^2\)
Q 14
The perimeter of a semicircle of radius \(r\) (including diameter) is \(\pi r + 2r\)
Q 15
The sum of the areas of the major segment and the minor segment of a circle equals the area of the circle.
Q 16
In this chapter, many problems involve finding areas of figures formed by combinations of circles with rectangles, triangles or squares.
Q 17
The length of the arc of a full circle of radius \(r\) is \(\pi r\)
Q 18
If the radius of a circle is tripled, its area becomes nine times.
Q 19
A sector with central angle \(180^\circ\) is called a semicircular region.
Q 20
A quadrant is a sector of a circle whose central angle is\(60^\circ\)
Q 21
The unit of circumference of a circle is always in square units.
Q 22
The unit of area of a circle is always in square units.
Q 23
For a fixed radius, the area of a sector increases as its central angle increases.
Q 24
In problems on circular paths around a circular field, the width of the path is the difference between the outer and inner radii.
Q 25
Every chord of a circle divides it into two sectors.
Key Takeaways — AREAS RELATED TO CIRCLES
Core facts for CBSE Boards & exams
1
Area of circle = πr²; Circumference = 2πr.
2
Area of sector = (θ/360) × πr², where θ is the central angle in degrees.
3
Length of arc = (θ/360) × 2πr.
4
Area of minor segment = Area of sector − Area of triangle.
5
Area of major segment = Area of circle − Area of minor segment.
6
For θ = 180°, the sector becomes a semicircle: area = πr²/2.