Circle definition states a shape that consists of points, in a two-dimensional plane, equidistant from a given point. A circle is a closed curve that has no corners or vertices. Many round shapes in our real life are defined by circles. In Mathematics, geometry is a branch that deals with the study of different shapes and their measurements. Basically, geometry is classified into two-dimensional geometry and three-dimensional geometry. Two-dimensional geometry deals with 2D shapes. It has only two measures, such as length and height. Circle, square, rectangle, etc., are examples of 2D shapes. Three-dimensional geometry deals with 3D shapes. It has length, height, and width. Cylinder, sphere, cube, cuboid are examples of 3D shapes. Here, let us discuss the circle definition, with its area and circumference/perimeter formula.

Circle Definition in Maths

A circle is defined as a two-dimensional figure, which is round in shape where all the points on the surface of the circle are equidistant from the center point is called “P”. The distance from point P to the surface of the circle is called the radius of the circle (R). The twice of radius of the circle is called the diameter (D = 2R). A circle has no straight edges or corners. Similarly, the semicircle is half of the circle and also a quarter circle is formed by splitting the circle into four equal parts.

Circle Formula

Since a circle is a two-dimensional figure, it has an area and a perimeter. Let us discuss the formula for area and the circumference of a circle.

Area of Circle 

The area of the circle is the space occupied by the shape circle. The formula to calculate the area is given by

Area of Circle, A = πr² Square units

Circumference of Circle:

Circle circumference is the enclosing boundary of any curved geometrical shape. The formula for the circumference of a circle is given by:

Circumference/ Perimeter of Circle = 2πr units

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Circle Definition Solved Examples

Question 1: Find the area and the circumference of a circle where the radius is 7 cm.

Solution:

Given: Radius, r = 7 cm

Now substitute the radius value in the formulas.

Area of Circle, A = πr² Square units

A = (22/7)× 7× 7

A = 22 × 7

A = 154 cm²

Circumference of Circle = 2πr units

C = 2× (22/7) × 7

C = 2 × 22

C = 44 cm

Therefore, the area and the circumference of the circle are 154 cm² and 44 cm, when the radius is 7 cm.

Question 2: If the radius of the circle is 3.5 cm, then find its area.

Solution: Given, radius of circle = 3.5 cm

By the circle definition, the formula for its area is:

A = πr² Square units

A = π (3.5)² Square cm

A = 39 sq.cm (approx.)

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