Circle Formula

What is a Circle?

A circle is the simplest closed curve, lying in a plane. A circle can be defined as a set of every point in a plane that is equidistant from a given central point. The fixed distance of such points from the center is called the radius, r, of the circle, while the point is called the center.. Diameter (d) is the line segment that passes through the center of the circle and touches two points on the boundary, which is also called the circumference.

Formulas Related to Circles

The Formulas of Circle are given as,

1. Diameter

The diameter is the longest distance across the circle, passing through the middle.

    D = 2r

where, r is the radius.

2. Circumference

The circumference is the distance around the circle.

C = 2πr

where, r is the radius & 

3. Area

The area is the space enclosed within the circle.

where r is the radius.

Solved Problems

Problem 1: A circle has a radius 8 cm. Calculate its diameter, area and circumference.

Solution:

Given parameters are,

 Radius, r = 8cm

Diameter of a circle is given by

 D =2r

    = 2 × 8 cm

    = 16 cm

Area of a circle,

         = π × 64

         = 201.088 cm2

Circumference of a circle,

       C =2 π r

           = 2 × π × 8

           = 50.272 cm

Problem 2: Find diameter, area and circumference of a circle of radius 15 cm.

Solution:

Given parameters are,

Radius of a circle, r = 15 cm

Diameter of a circle,

   D = 2r

      = 2 × 15

      = 30 cm

Area of a circle ,

      

       = π × 225

     

       = 706.95 

Circumference of a circle,

      C = 2 π r

         = 2 × π × 15

         = 94.26 cm