If the radius of a circle is increased by 75%, then its circumference will increase by :

Solution (By Examveda Team)

Let original radius be R cm
Then, original circumference = $$2\pi r$$ cm
New radius :
$$\eqalign{ & = \left( {175\% {\text{ of }}R} \right)cm \cr & = \left( {\frac{{175}}{{100}} \times R} \right)cm \cr & = \frac{{7R}}{4}\,cm \cr} $$
New circumference :
$$\eqalign{ & = \left( {2\pi \times \frac{{7R}}{4}} \right)cm \cr & = \frac{{7\pi R}}{2}\,cm \cr} $$
Increase in circumference :
$$\eqalign{ & = \left( {\frac{{7\pi R}}{2} - 2\pi R} \right)cm \cr & = \frac{{3\pi R}}{2}\,cm \cr} $$
Increase % :
$$\eqalign{ & = \left( {\frac{{3\pi R}}{2} \times \frac{1}{{2\pi R}} \times 100} \right)\% \cr & = 75\% \cr} $$