Question

if the radius of a circle is increased by 75% then its circumference will increase by

Answer 1

Let the radius be x units.

Therefore, Increased radius = x+x×75100=7x4x+x×75100=7x4

Original circumference = 2πx2πx

Increased circumference = 2π×7x4=14πx42π×7x4=14πx4

= 7πx27πx2

Therefore, Increase in circumference = 7πx2−2πx7πx2−2πx

= 3πx23πx2

Therefore, Percentage increase = 3πx22πx×1003πx22πx×100

=75%

Hope it helps you.