Question

If the radius of a circle is increased by 50% then the area of the circle is increased by ?

• A. 125%
• B. 100%
• C. 75%
• D. 50%

Answer 1

The correct option is A 125%

Let the radius = r units. Then Area, = $\pi r^2$
Increased radius = $\frac{150}{100}r=1.5runits$
$\therefore$ Increased area = $\pi \times (1.5r{)}^2=2.25\pi r^2$
% increase $=(\frac{2.25\pi r^2-\pi r^2}{\pi r^2}\times 100)$%
$=\left(1.25x100\right)$ % $=125$ %