Question

How to find area of circle?

Answer 1

Let there be a circle of radius ${}^{\prime }{a}^{\prime }$.

Take a ring of radius $r$ and thickness $dr$

Area of ring = Perimeter $\times$ thickness

$\Rightarrow dA=2\pi rdr$

Total area of circle

$\Rightarrow \int dA={\int }_0^{a}2\pi rdr$

$\Rightarrow A=2\pi {\left[\frac{r^2}{2}\right]}_0^a$

$\Rightarrow A=\pi r^2$