Areas Related to Circles — Chapter Summary
Gujarat Board · Class 10 · Mathematics
Summary of Areas Related to Circles for Gujarat Board Class 10 Mathematics. Part of the Gujarat Board Class 10 Mathematics syllabus.
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Overview
This chapter focuses on understanding and calculating areas of different parts of a circle, specifically sectors and segments. Building upon your knowledge of basic circle properties, you will learn to find areas of portions of circles that are commonly encountered in real-life applications and comp
Key Concepts
A sector is the portion
A sector is the portion of a circular region enclosed by two radii and the corresponding arc. It looks like a slice of pizza. The angle between the tw
A segment is the portion
A segment is the portion of a circular region enclosed between a chord and the corresponding arc. It is the area cut off by a chord. Minor segment is
Area of sector = (θ/360°) ×
Area of sector = (θ/360°) × πr², where θ is the angle in degrees and r is the radius. This formula is derived using unitary method, considering that a
Length of arc = (θ/360°) ×
Length of arc = (θ/360°) × 2πr, where θ is the angle in degrees and r is the radius. This gives the curved boundary length of a sector.
Area of segment = Area
Area of segment = Area of corresponding sector - Area of corresponding triangle. This involves calculating the sector area first, then subtracting the
Learning Objectives
- Understand the concepts of sector and segment of a circle
- Distinguish between minor and major sectors and segments
- Learn to calculate the area of a sector using the angle and radius
- Find the length of an arc corresponding to a sector
- Calculate the area of a segment using sector and triangle areas
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Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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