Areas of figures are the spaces occupied within the boundaries of the flat figures. Whether the figure is a square, a rectangle, a triangle or a circle, the basic concept of the area remains the same for all closed 2-d shapes though the formulas are different in each case. Among all these, the area of circle formula sounds a bit tough to understand and memorize. So, in this article, the concept will be explained in detail and with appropriate steps and examples to make it easier to be learnt.
Area of circle
The extent covered inside any curved line which is at equal distance at all the points from a certain (fixed) point in the exact middle (centre) of the figure is the area of the circle. The circle do not have any corners or vertices. The Circle’s area formula can be summed up as:
Case 1
- When the radius is given in the questions, Area of circle= π×r^2
Case 2
- When the diameter is provided in the questions, Area of circle=π/4×d^2
Case 3
- When only the circumference is known, Area of the circle=(C^2)/4π
To understand and memorize the above relations it is necessary to understand the concept of area in detail.
Steps to learn the formulas for area of circle easily
It is well known that understanding the concept makes the application easy. These are simple steps that may help you to recall the concept and relations every time you need them.
Case 1. When the radius is given and you are required to calculate the area
Step 1. Identify the radius
In a circle, the distance between the centre (fixed point in the middle of the figure) and the boundary is said to be the radius of the respective circle. Radius is often represented by the alphabet ‘r’ or ‘R’.
Step 2. Knowing the value of pi (π)
The pi (symbol π) is a mathematical constant and its value is always taken as 3.14 in decimal or 23/7 in fraction.
Step 3. Introducing the values of the radius and pi in the formula
Let’s now understand this with an example.
Example: Calculate the area of a circle whose radius is 3 cm.
Solution: Here r= 3 cm.
Area of circle= π×r^2
Substituting the value of r in the formula
Area = 3.14× (3) ^2 = 3.14×3×3 = 3.14×9= 28.26 sq. cm.
Case 2. When the diameter of the circle is given and area is to be obtained
Step 1. Identifying the diameter
As the concept of the radius is already explained the diameter can be taken as twice the value of the radius, i.e., d= 2*r. The diameter is the longest chord of any circle passing through the center and touching the boundary at both ends.
Step 2. Recalling the value of π
Step 3. Applying the values in the relation.
Example: Calculate the area of the circle when the diameter of the same is 6cm.
Solution. There can be two solutions to this question
If d= 6cm.
Then r= 6/2= 3 cm.
Then substituting the value of r in Area= π*r^2= 3.14*(3) ^2= 28.26 sq. cm.
Or,
If d= 6cm
Then substituting the values directly in the formula Area= π/4*d^2
Required area= (3.14/4) * 6^2= (3.14/4) *6*6= 28.26 sq. cm.
It is seen that the same results are obtained using both methods.
Case 3. How to find the area of the circle if the circumference is given
Step 1. Identify the circumference
The circumference is the measurement of the boundary of the circle. The formula for the circumference of the circle is C=2πr.
Step 2. Recalling the values and substituting them in the formulas.
There are two methods of calculating the area through the circumference of the circle. The first one is the traditional old method: find the radius using the circumference and then use that radius to obtain the area. Second is the direct use of the relation using the circumference and calculating the area. Thus, the concept and formulas of the area can be used and remembered easily. Cuemath experts explain the related topics with the details about the equation of circle which is used in coordinate geometry.
Example: Get the area of the circle whose circumference is 44 cm.
Solution: First method
If C = 44cm.
Then r=7*C/44=7*44/44= 7 cm.
Next Area = π×r^2= 3.14*7*7= 153.86 sq. cm.
Or,
Direct application of the formula
Area = C^2/4π= 44^2/ (4*3.14) = 153.86 sq. cm.
