Question

The radius of circle is increased by 1%.Find how much % does its area increases

Answer 1

Answer:

let radius be r

therefore area

$\pi \: r {}^{2}$

if r increased by 1 percentage

than radius= r+r*1/100=(101/100)r

area=

$\pi \times (101 \div 100) {}^{2}r {}^{2} \\ \\ 10201\pi r {}^{2} \div 10000$

area increased =

$201\pi \times r { }^{2} \div 10000$

$201\pi \times r { }^{2} \times 100 \div 10000\pi \times r {}^{2}$

$201 \div 100 \\ \\2.01\%$