Question

If the circumference of a circle is reduced by 50 % then the area will be reduced by

• A. 50%
• B. 25%
• C. 75%
• D. 12.5%

Answer 1

The correct option is C 75%

Let radius of circle is r cm

Then circumference of circle =$2\pi r$

And area of circle= $\pi r^2$

If circumference of circle reduced 50%

Then new circumference of circle =$2\pi r\times \frac{50}{100}=\pi r$

So radius of new circle =$\frac{r}{2}$

And are of new circle=$\pi \left({\frac{r}{2}}^2\right)=\pi \left(\frac{r^2}{4}\right)$

Then reduced in area =$\pi r^2-\frac{\pi r^2}{4}=3\pi r^2$

So % reduced in area =$\frac{3\pi r^2}{\pi r^2}\times 100=75$ %