Circumference and Area of Circle
The circumference (perimeter) of a circle is 2πr and its area is πr2, where r is the radius of the circle and π is a constant equal to the ratio of circumference of a circle to its diameter.
A great Indian mathematician Aryabhata (476 - 550 AD) gave the value of π which is equal to 3.1416 correct to four places of decimals. However, for practical purposes, the value of π is generally taken as 22/7 or 3.14 approximately.
Circumference of Circle
Wrap a thread around any circular object so that the thread may not be loose and overlap. Measure this by a measuring scale as the thread is linear. This is approximately the circumference of the circular object.
For any circle, the ratio of c/d is same and this is denoted by π.
Circumference / Diameter = π
Circumference = π × Diameter
Circumference of circle = 2 × π × radius
π = 22/7 or π = 3.14
Example 1: Find the circumference of circle when radius is 3.5 cm.
Circumference = 2πr
Circumference = 2 × 22/7 × 7/2
= 22 cm
Example 2: The radii of two circles are 18 cm and 10 cm. Find the radius of the circle whose circumference is equal to the sum of the circumferences of these two circles.
Let the radius of the circle be r cm. Its circumference = 2πr cm.
Sum of circumferences of the two circles = (2π × 18 + 2π × 10) cm
= 2π × 28 cm
Therefore, 2πr = 2π × 28
r = 28 cm
Area of Circle
Area of circle = π × (radius)2
Example 3: There is a circular path of width 2 m along the boundary and inside a circular park of radius 16 m. Find the cost of paving the path with bricks at the rate of Rs.24 per m2. (Use π = 3.14)
Let OA be radius of the park and shaded portion be the path.
OA = 16 m
OB = 16 m - 2 m = 14 m
Area of the path = (π × 162 - π × 142) m2
= π(16 + 14)(16 - 14) m2
= 3.14 × 30 × 2 = 188.4 m2
So, cost of paving the bricks at Rs.24 per m2
= Rs.24 × 188.4 = Rs.4521.60