In Mathematics particularly in Geometry, a circle is a unique kind of ellipse in which the eccentricity is zero and the two foci are concurrent. A circle is also defined as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is termed its radius. Diameter is the line that divides the circle into two equal parts and is also equal to twice the radius i.e Diameter = radius*2.
In simple terms, a circle is a basic 2D shape that is measured in terms of its radius. The circles divide the plane into two regions as the interior and exterior regions. It is identical to the type of line segment. Assume that the line segment is bent around till both its ends join. Circles can be glimpsed in our surroundings as well sun, moon, ceiling fan, and so on.
Circumference
The perimeter of the circle is also called the circumference, which is the total length of the boundary of the circle. The circumference of a circle is the product of the mathematical constant π(Pi) and diameter.
The value of π = 3.1415926535897…
π or pi is a Greek letter. It is an important constant in mathematics. It gives the ratio of circumference to the diameter of a circle or the ratio of circumference to the diameter. For any given circle, this ratio will remain constant i.e π.
As the number is infinite, using an infinite number will make calculations nearly impossible. Therefore, for calculations, we use π = 22/7 or π = 3.14.. Making the calculations more straightforward.
The circumference is a linear value and its units are equal to the units of length.
Circumference of a Circle
- The circumference is defined as the distance around a circle or the length of a circle.
- The mathematical constant π(Pi) is the ratio of the circumference of a circle to its diameter and is approximated to the value π = 22/7or 3.14
- If the radius of a circle is extended further till it touches the boundary of the circle, it eventually becomes the diameter of a circle. Therefore, Diameter = 2 × Radius.
- The circumference of a circle can be calculated using the radius or diameter.
- Circumference formula = π× Diameter (using diameter)
- Circle Circumference = 2πr (using radius).
Circumference of Circle Formula
One of the important metrics of a circle is its circumference.
Here,
C = circumference
r = radius
d = diameter
Π = 22/7 or 3.14
1) When only radius(r) is given, C = 2πr
2) When only diameter(d) is given, C = πd
Examples
Example 1
If the radius of a circle is 40cm then determine the circumference of the circle.
Solution:
Given, the radius of the circle = 40cm.
Circumference of a circle formula = 2πr
Substituting the values in the formula,
2×(22/7)×40 = 251.2cm.
Therefore, the circumference of the circle is 251.2cms.
Example 2
The perimeter of a rectangular rod is 210m. The same rod is curved into the shape of a circle. Find the radius of the circle formed using the circumference given.
Solution:
The perimeter of the rectangle = Total length of the rod utilized = Circumference of the circle formed.
Hence, the Circumference of the circle formed = 210m
Circumference of a circle formula = 2πr
Circumference of the circle = 210
Substituting the values in the formula,
210 = 2πr
210 = 2×(22/7)×r
Therefore, the radius of the circle formed using the rod is 33.5m.
Practice Problems
Solve the following circle problems:
- Find the circumference of a circle whose radius is 120cm
- If the circumference of a circle is 60cm, find the radius of this circle.
- If the circumference of a circle is 180cm, find the diameter of this circle.
To know more about the topic, visit Cuemath to book a free session.