Subject: General Aptitude · Chapter: Area · Exam: 2010 · Marks: · Difficulty:
A square is inscribed in a circle and another in a semi-circle of same radius. The ratio of the area of the first square to the area of the second square is
(a)2 : 5
(b)5 : 2
(c)4 : 5
(d)5 : 4
Answer
Answer (as printed): B
Explanation
Let the radius of each of the circle and the semi-circle be $r$ units. Diagonal of the first square $=(2 r)$ units. Let the side of the second square be $a$ units. Then, $r^{2}=a^{2}+\left(\frac{a}{2}\right)^{2} \Rightarrow r^{2}=\frac{5 a^{2}}{4} \Rightarrow a^{2}=\frac{4 r^{2}}{5}$. ∴ Ratio of the areas of the two squares $$=\frac{\frac{1}{2} \times(2 r)^{2}}{a^{2}}=\frac{2 r^{2}}{\left(\frac{4 r^{2}}{5}\right)}=\frac{5}{2}=5: 2 .$$
Explanation as extracted from the printed page; notation may be imperfect.