Areas related to Circles

Areas related to Circles:

Perimeter and Area of a Circle — A Review

The distance covered by travelling once around a circle is its perimeter,
usually called its circumference.

In other words, circumference diameter = π
or, circumference = π × diameter
= π × 2r (where r is the radius of the circle)
= 2πr

Let us recall the concepts learnt in earlier classes, through an example.
Example 1 : The cost of fencing a circular field at the rate of Rs 24 per metre is
Rs 5280. The field is to be ploughed at the rate of Rs 0.50 per m2. Find the cost of
ploughing the field (Take π =22/7).
Solution : Length of the fence (in metres) =
Total cost Rate = 5280 = 22024
So, circumference of the field = 220 m
Therefore, if r metres is the radius of the field, then
2πr = 220
or, 2 ×
22
7 × r = 220
or, r =
220 × 7
2 × 22 = 35
i.e., radius of the field is 35 m.
Therefore, area of the field = πr2 =272
× 35 × 35 m2 = 22 × 5 × 35 m2
Now, cost of ploughing 1 m2 of the field = Rs 0.50
So, total cost of ploughing the field = Rs 22 × 5 × 35 × 0.50 = Rs 1925

Areas of Sector and Segment of a Circle:

The circular region enclosed
by two radii and the corresponding arc is called a
sector of the circle and the portion (or part) of the
circular region enclosed between a chord and the
corresponding arc is called a segment of the circle.