Subject: General Aptitude · Chapter: Area · Exam: 2009 · Marks: · Difficulty:
If the radius of a circle is increased by 200\%, then its area will increase by
(a)200\%
(b)400\%
(c)800\%
(d)900\%
Answer
Answer (as printed): C
Explanation
Let the original radius be $R$. New radius $=(100+200) \%$ of $R=300 \%$ of $R=3 R$. Original area $=\pi R^{2}$; New area $=\pi \times(3 R)^{2}=9 \pi R^{2}$. Increase in area $=\left(9 \pi R^{2}-\pi R^{2}\right)=8 \pi R^{2}$. $$\text { ∴ } \text { Increase } \%=\left(\frac{8 \pi R^{2}}{\pi R^{2}} \times 100\right) \%=800 \% \text {. }$$
Explanation as extracted from the printed page; notation may be imperfect.