Question

If the radius of the circle is increased by $50\%$ then by how much percent the area of the circle is increased?

• A. $125\%$
• B. $100\%$
• C. $25\%$
• D. $75\%$

Answer 1

Answer: (A)

$125\%$

Let the radius of the circle $=r$ units
Then original area $=$ $\pi r^2$
Increased radius $=$ $r+50\%$ of $r=r+\frac{50r}{100}=\frac{150r}{100}=1.5r$
$\therefore$ New area $=\pi {\left(1.5r\right)}^2=2.25\pi r^2$
$\therefore$ $\%$ Increase $=$ $(\frac{2.25\pi r^2-\pi r^2}{\pi r^2}\times 100)$ $\%=(\frac{1.25\pi r^2}{\pi r^2}\times 100)\%$
$=(1.25\times 100)\%=125\%$