Subject: General Aptitude · Chapter: Area · Exam: 2004 · Marks: · Difficulty:
The ratio of the circumferences of two circles is 2 : 3. What is the ratio of their areas?
Answer
Answer (as printed):
Explanation
Let the radius of the circle be $r$ and $R$ respectively. $$\text { Then, } \frac{2 \pi r}{2 \pi R}=\frac{2}{3} \Rightarrow \frac{r}{R}=\frac{2}{3} \Rightarrow \frac{r^{2}}{R^{2}}=\left(\frac{2}{3}\right)^{2} \Rightarrow \frac{\pi r^{2}}{\pi R^{2}}=\frac{4}{9} \text {. }$$ Hence, ratio of areas $=4: 9$.
Explanation as extracted from the printed page; notation may be imperfect.