Areas Related to Circles

Board: GSEB Class: 10

Chapter Overview

The perimeter (circumference) of a circle is 2pi r, and the area is pi r². A sector is the region bounded by an arc and two radii. Area of sector = (theta/360) x pi r², where theta is the central angle in degrees. Length of arc = (theta/360) x 2pi r. A segment is the region bounded by an arc and a chord. Area of segment = area of sector - area of triangle. Combined figures involve finding perimeters and areas of shapes formed by combining circles with other plane figures.

Topics Covered

Circumference
Area of Circle
Arc Length
Area of Sector
Area of Segment
Combined Figures
Shaded Region Problems

Key Formulas

Circumference = 2pi r

Area = pi r²

Arc length = (theta/360) x 2pi r

Sector area = (theta/360) x pi r²

Segment area = sector area - triangle area

Real-World Applications

Applications: Circular park design, wheel manufacturing, pizza/circular object pricing, architectural domes.

Study Tips

Tip: Learn sector and segment formulas separately

Tip: Practice shaded area problems

Tip: Draw figures for combined shapes