# Circumference Formula

## Circumference Formula

In Circumference in geometry means “carrying around” and can refer to a circle or an ellipse. Essentially, the circumference would be the length of the arc if the circle were widened and straightened out into a line segment. A closed figure’s perimeter is the length of its curve. Also known as the edge of a disk, circumference refers to the circle itself. Any great circle on a sphere has a circumference, or length, equal to its circumference.

## Formula to Find Circumference

When distance is defined in terms of straight lines, as in many elementary treatments, the Circumference Formula of a circle cannot be used as a definition. As the number of sides of an inscribed regular polygon increases without bound, the circumference of a circle may be defined as the limit of their perimeters. Circumference is used both to measure physical objects and to describe abstract geometric shapes.

### Circumference Formula in Terms of Area

A circle’s Circumference Formula can be expressed as follows:

The method for approximating π has been used for centuries, with increasing accuracy resulting from the use of polygons with larger and larger sides. Christoph Grienberger performed the last calculation using polygons with 10 40 sides in 1630. Some authors use Circumference Formula to denote an ellipse’s perimeter. An ellipse’s circumference cannot be calculated using only elementary functions using the semi-major and semi-minor axes. In terms of these parameters, there are, however, approximate formulas.

### Solved Examples

1. A wheel rotates 5000 times to cover 10 km. Calculate the wheel’s radius.

The solution is:

The number of rotations is 5000.

The total distance covered was 10 kilometres

The radius of the wheel is ‘r’.

Wheel Circumference Formula = distance covered in one rotation = 2πr.

The distance covered in 5000 rotations equals 10 km = 1000000 cm.

Therefore, in 1 rotation, the distance covered is

1000000/5000cm=200cm

But this is equal to the Circumference Formula. Hence, 2πr = 200 cm

r = 200/2π

r = 100/π

Based on the approximate value of π as 22/7, we get

r = 100 × 7/22

r = 31.82 cm approx.

1. Semicircular shapes have a diameter of 14 cm. In this shape, what is the perimeter?

Solution:

Given,

14 cm is the diameter of the semicircle.

The radius of the circle is equal to r = d/2 = 14/2 = 7 cm

Perimeter of semicircle = (Perimeter of circle/2) + d

= (2πr/2) + d

= πr + d

= (22/7) × 7 + 14

= 22 + 14

= 36 cm