Areas related to circles:
The chapter 'Areas related to circles' carrying the weightage of 3-4 marks in the board examination. It covers the concepts like, area of sector, area of segment, arc length, perimeter of sector.
Most possible variation of question types that we can expect in board exam as per previous year question paper are discussed below.
| Total Marks 3 to 4 | |
| Variation 1 | Varaition 2 |
Total marks = 4
|
Total marks = 3
|
To prepare well for the borad examination, it is necessary to understand the following concepts clearly.
- Area of sector - Area of minor sector and major sector, area of shaded region
- Area of segment - Area of major segment and minor segment
- Perimeter of sector
- Arc length
| Important Concept(Learning Outcomes) | Expected question Type | Concept dealt with |
| Area of sector | Sec C, Sec D | |
| Area of segment | Sec C | Area of major and minor segment |
| Arc length and perimeter of sector | Sec A, Sec B |
Let us recall the concepts in area related to circles:
1. Area of a sector \(= \frac{\theta}{360°}\times \pi r^2\)
2. Area of minor sector \(=\) Area of circle \(-\) Area of major sector
3. Area of major sector \(=\) Area of circle \(-\) Area of minor sector
4. Length of an arc as a sector \(= \frac{\theta}{360°}\times 2\pi r\)
5. The perimeter of the sector \(= 2r +2 \pi r \frac{\theta}{360}\)
6. Area of segment of a circle \(=\) Area of the corresponding sector \(-\) Area of Corresponding triangle
7. Area of Minor segment \(=\)
8. Area of major segment \(=\) Area of circle \(-\) Area of minor segment
Common mistakes to avoid:
1. using the wrong formula, remember the difference between the formulas of area of circle, circumference, area of sector and length of the arc.
2. Confusing the sector and segment: Sector is bounded by two radii and an arc, whereas segemnt is bounded by chord and an arc.
3. For a sector, always check the central angle before applying the formula.
4. Using the wrong value of \(\pi\): Use the value specified in the question. If none is given, use the standard value required by the calculation.
5. Adding areas when subtration is required: In shaded-area questions, carefully identify whether the required region is an addition or difference of areas.
Exam tips & tricks:
1. Know the key formulas.
2. For clock problems: Convert time into the central angle first, then use the sector/arc formula.
3. Break complex figures into simple shapes: Find each area separately and add or subtract as required.
Use addition when the total areas is made of two or more separate region that don't overlap
Use subtraction when a shape is inside another shape and you only need the space leftover around it
4. Areas must be written in square units such as \(cm^2\) or \(m^2\).