The area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr^{2}, (Pi r-squared) where r is the radius of the circle. The unit of area is the square unit, such as m^{2}, cm^{2}, etc.
Calculation of Area of Circle
For example, if the radius of circle is 7cm, then its area will be:
Area of circle with 7 cm radius = πr^{2} = π(7)^{2} = 22/7 x 7 x 7 = 22 x 7 = 154 sq.cm.
Also, if we know the circumference of the circle, then we can find the area of a circle.
How?
Since, the circumference is 2 times of product of pi and the radius of the circle, such as:
C = 2πr
Therefore, here we can find the value of the radius,
r = C/2π
Once, we have evaluated the value of the radius, we can easily find the area.
What is the area of this circle?
Radius = r = 3
Area | = π × r^{2} | |
= π × 3^{2} | ||
= π × (3 × 3) | ||
= 3.14159… × 9 | ||
= 28.27 (to 2 decimal places) |
How to Calculate the Area
The area of a circle is:
Radius Of A Circle And Chord
The radius of a circle is the distance from the center of the circle to any point on its circumference. It is usually denoted by ‘R’ or ‘r’. This quantity has importance in almost all circle-related formulas.
Radius Formula
Concerning area and circumference, we can write the formula for the radius as:
R = C/2π And R = √(A/π)
Also, R = D/2 |
Solved Examples
Let us see some solved problems on the radius and chord of a circle.
Example 1: Find the radius of the circle if its diameter is 16 cm.
Solution:
Given,
Diameter of circle = 16 cm
Radius of circle = Diameter/2
= 16/2
= 8 cm