Subject: General Aptitude · Chapter: Area · Exam: 2015 · Marks: · Difficulty:
Two equal circles are drawn in square in such a way that a side of the square forms diameter of each circle. If the remaining area of the square is $42 \mathrm{cm}^{2}$. How much will the diameter of the circle measures?
(a)3.5 cm
(b)4 cm
(c)14 cm
(d)7.5 cm
Answer
Answer (as printed): C
Explanation
Let length of each side of square $=2 \pi$ According to the question, $\frac{\pi r^{2}}{2}+\frac{\pi r^{2}}{2}+42=$ Area of square $\Rightarrow \pi r^{2}+42=4 r^{2}$ $\Rightarrow 4 r^{2}-\pi r^{2}=42$ $\Rightarrow r^{2}\left(4-\frac{22}{7}\right)=42$ $\Rightarrow r^{2}\left(\frac{28-22}{7}\right)=42$ $\Rightarrow \frac{6 r^{2}}{7}=42$ $\Rightarrow r^{2}=\frac{42 \times 7}{6}$ $\Rightarrow r^{2}=7 \times 7$ $\Rightarrow r=7$ $\therefore 2 r=14 \mathrm{cm}$