AREAS RELATED TO CIRCLES
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.
An arc is a continuous portion of the circumference of a circle.
Both arc length and sector area are proportional to the central angle of the sector.
Areas are measured in square units such as \(\text{cm}^2), (\text{m}^2), or (\text{km}^2\).
Yes, since radius is half of the diameter, it can be substituted accordingly.
The area becomes four times because area is proportional to the square of the radius.
It helps in solving problems related to fields, tracks, wheels, gardens, roads, and circular designs.
It extends mensuration concepts from polygons to curved figures.
Numerical problems on sectors, segments, shaded regions, and word problems based on real-life situations.
Only basic geometric tools like compass and ruler are used for diagrams, not for constructions.
Area subtraction and proportional scaling are the main mathematical transformations used.
Because a segment is obtained by removing a triangular portion from a sector.
By keeping units consistent, using correct values of \(\pi\), and identifying the correct region.
No, understanding the relationship between angles and areas is essential.
It involves finding the area of specific parts of a circle shown as shaded in a figure.
By drawing diagrams, identifying known values, and applying appropriate formulas step by step.
Diagrams help visualise sectors, segments, and shaded regions accurately.
It helps relate angles to areas and simplifies calculations.
Yes, real-life based circular layouts are often used in case-study problems.
Basic understanding of circles, triangles, and area formulas.
It builds a foundation for advanced geometry and trigonometry involving circles.
It represents the complete angle around the centre of a circle.
By rounding values properly and following standard calculation steps.
Practising a variety of numerical problems and mastering formula application.
Yes, especially involving composite figures and logical reasoning.
Because it combines geometry, algebra, proportionality, and real-life application.
