Circumference of circle = π * Diameter = π * 2*Radius

π is an irrational number and its decimal expansion is non-terminating and non-recurring (non-repeating). We generally take the value of π as 22/7 or 3.14

Area of Circle = π * Radius * Radius = πr2

Numerical: Archery target marked with its five scoring regions from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find area of each of five scoring regions.

Solution:

Radius of Gold Circle is 10.5 cm, thus area of gold circle = πr2

Or Area = π(10.5)2 = 346.5 cm2

Area of the red Zone = Area of red circle – Area of Gold circle

Or Area of red Zone = π(21)2 – π (10.5)2

Or Area of red zone = 1039.5 cm2

Similarly you can find area of all the zones.

Area of Sector & Segment

Part of the circular region enclosed by two radii and the corresponding arc is called a sector of the circle.

Part of the circular region enclosed between a chord and the corresponding arc is called a segment of the circle.

When we write ‘segment’ and ‘sector’ we will mean the ‘minor segment’ and the ‘minor sector’ respectively, unless stated otherwise.

Areas of Combination of Plane figures

Area of figure = Sum of areas of smaller parts

Numerical: From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut. Find area of remaining portion of the square.

Solution:

Required area = Area of Square -4 (1/4 area of circles A) – Area of circle B