Question

Why do we use $\pi$ for finding area of a circle ?

Answer 1

In Geometry, for computing the area, perimeter or any other property of a certain shape, we need to depend upon the dimensions of the shape.

For example,In case of a Square, we depend on its side length. In case of a Rectangle, we use its length and breadth.

Circle being a curved shape, it was difficult to depend upon a certain dimension. It was observed that the circles' area and circumference depends upon its diameter.

Initially, the circles' circumference was measured roughly using threads. The ratio of the circumference and the diameter, $i.e.\left(Circumference/Diameter\right)$ among the circles was observed to be similar but not equal.

Aryabhatta defined the irregularity of this ratio to be an irrational number. He also found the value of this ratio upto five significant as pi.

$i.e.\pi =\left(Circumference\right)/\left(Diameter\right)$

Hence,

$Circumference=\pi \ast Diameter=\pi \ast 2\left(Radius\right)$

And also, $Area=\left(Circumference/2\right)\ast Radius$

$=\pi \left(Radius\right)\ast Radius$

$=\pi \ast \left(Radius\right)²$