Area Of A Circle Formula

Area of a Circle Formula- The two-dimensional space enclosed by a circle is measured as its area. The radius of the circle is the primary factor in determining its size. The area of a circle is calculated using the formula A = πr², where r represents the circle’s radius. Area is measured in square units such as m2, cm2, in2, and so on. The area of a circle formula is useful for determining the area occupied by a circular field or plot.  Let us study how to find the area of a circle using formulae and examples.

Area of a Circle Formula

A circle is a rounded shape made up of points that are equally spaced apart from one another and its center. The centre of the circle is the location from which the radius is calculated. The distance between any two points on a circle’s surface and its centre is its radius. The length of one diameter would be equal to two radii placed end to end in a circle. Modern mathematics can calculate the area using integral calculus or its more complex descendant, real analysis.

As a result, a circle’s diameter is twice as long as its radius. The number of square units contained within a circle is its area.  A circle has the largest area for a given perimeter and the smallest area for a given perimeter. The circumference of a circle is equal to its perimeter C. Every geometrical shape has a defined area. The region that the shape occupies in a 2D plane is what this area is known as. When discussing a circle’s Area Of A Circle Formula, one has to refer to the area on a 2D plane that is completely covered by the circle’s radius. The formula that can be used to determine the circle’s area is the Area Of A Circle Formula.

The area of a circle is the amount of space encompassed by its round form. It is the entire area covered by the circle inside its limits. The formula for calculating the area of a circle is:

Area of Circle = πr²

Area of Circle = πd² / 4

where,
r = radius of circle
d is diameter of circle
π = 22/7 or 3.14

The area of circle formula is useful for calculating the areas of circular fields or plots. It is also useful to determine the area covered by circular furniture and other circular objects.

What is a Circle

All points in a plane that are at a specific distance from a specific point, called the centre, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

Radius

The radius of a circle is the distance between any two points on the circle and its centre. The radius must typically be a positive integer.

Diameter

Diameter is the length of a line segment whose endpoints are on the circle and which passes through its centre. The maximum distance exists between any two locations on the circle at this time. It is a unique instance of a chord, specifically the longest chord for a particular circle, and its length is double the radius. The diameter of a circle is equal to the length of the rope that encircles it.

Circumference

The circumference of a circle is the total distance travelled in making one full turn around it. The complete length of a closed figure’s boundary is referred to as the figure’s perimeter. The perimeter has a distinct name when it comes to circles. It is referred to as the circle’s “circumference.” The whole length of the circle’s boundary is known as its circumference. The circumference of a circle can be found by opening it up and drawing a straight line; this yields the length of the circle.

The circumference of a circle is the entire length of its border; hence, the perimeter of a circle is referred to as its circumference. The formula for the circumference of a circle is C = 2πr.

What is the Area of a Circle?

In geometry, the Area of A Circle Formula is equal to r2 when surrounded by a circle of radius r.Here, the Greek letter ℼ stands for the constant proportion of a circle’s circumference to its diameter, which is roughly equivalent to 3.14159. This Area Of A Circle Formula, which was first discovered by Archimedes, can be derived by considering the circle as the boundary of a series of regular polygons. The method for calculating a regular polygon’s area reads “the area is half the perimeter times the radius.” For a circle, it reads “the area is half the perimeter times the distance from the centre to the sides.”

How to find the Area of a Circle?

The following are the steps required to calculate the area of a circle:

Step 1: Mark the circle’s radius.

Step 2: Use the formula A = πr2, where r is the radius and π is the constant with an approximate value of 3.14.

Step 3: The required circle area is determined by the result obtained in Step 2. It’s measured in square units.

If the diameter of a circle is known, it is first converted to the radius using the relation,

Diameter = Radius / 2

Solved Example

Example 1: A ball has a radius of 5 units. Calculate its area?

Solution: We can use circle formulae to calculate the area of the ball..

given, r = 5 units, π = 3.14

Area = πr²

Area = 3.14 × 5 × 5
Area = 78.50 unit²

Thus, the area of the ball is 78.50 units²

Example 2: If the rope is circular with a diameter of 3 units. Calculate the area.
Solution: We know that rope is in circular shape, and its diameter = 3 units and π = 3.14

Area = (π/4) × d²  

Area = (3.14 /4) × 3 × 3
= 7.065 units²

Therefore, the area of the rope is 7.065 units²

Example 3: If the circumference of the circle is 4 units. Find its area.

Solution: Circumference of the circle = 4 units and π = 3.14

Area  = C²/4π

Area = 4 × 4 / (4 × 3.14)
= 1.274 units²

Therefore, the area of the circle is 1.274 units²

Solved examples on the Area Of A Circle Formula are available on the Extramarks website as well as the mobile application.