Question

What is the equation for circumference?

Answer 1

Hint: Circumference is the topic of geometry. And we calculate the circumference of the circle. A circle is a closed two dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. In geometry, the circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. Or we can say the perimeter is the curve length around any closed figure.

Complete step by step solution:
Let's draw a circle of radius $r$ having diameter $d$ with center A.

Where $AB=r$ (radius of the circle) and $CD=d$ (diameter of the circle) and $c$ is the circumference of the circle.
The area of the circle is $\pi {{r}^{2}}$ where $r$ is the radius of the circle.
The circumference of the circle is $\pi d$ where the value of $\pi $ is either $3.14$ or $\dfrac{22}{7}$ and $d$ is the diameter of the circle.
We know the diameter can be written in term of $r$ (radius of the circle) as:
$\Rightarrow d=2r$
So we can write the circumference of the circle as:
$\Rightarrow c=2\pi r$
If we write the value of the $\pi $ in the circumference of the circle we get:
$\Rightarrow c=2\cdot 3.14\cdot r$
Hence the equation of the circumference of the circle is $c=2\pi r$.

Note: We have to find circumference of a circle. Pi comes here in the circumference because of its ratio. 2 and r comes because it equals the diameter as I discussed above. So Pi times 2 times r is circumference over diameter times diameter which gives circumference.