The radius of a circle is increased by 1%. How much does the area of the circle increase?

Area of circle with radius of 

x$x$ length is π$\pi$ ∗x2$\ast x^2$

If radius is increased by 1%$1\mathrm{\%}$ , it's new length will be 

x+x100=101x100=1.01x$x+\frac{x}{100}=\frac{101x}{100}=1.01x$ and the new area will be π∗$\pi \ast$ 

(1.01x)2=π∗$(1.01x{)}^2=\pi \ast$ 1.0201x2$1.0201x^2$.

π∗$\pi \ast$ 1.021x2−π∗$1.021x^2-\pi \ast$ x2=π$x^2=\pi$ x2(1.0201−1)$x^2(1.0201-1)$

=π$=\pi$ x2∗0.021=0.0201∗100=2.01$x^2\ast 0.021=0.0201\ast 100=2.01$

So the area of circle will increase by 2.01%