Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
The circumference of a circle is 10\% more than the perimeter of a square. If the difference between the area of the circle and that of the square is $216 \mathrm{cm}^{2}$, how much does the diagonal of the square measure? (in cm) [CET-Maharashtra (MBA), 2016]
(a)$14 \sqrt{2}$
(b)14
(c)20
(d)$20 \sqrt{2}$
Answer
Answer (as printed): D
Explanation
Let the radius of circle be $r \mathrm{cm}$ and side of square be a cm. Then circumference of circle $$=2 \pi r \text { and perimeter of square }=4 a$$ According to the question, $2 \pi r=4 a \times \frac{110}{100}$ $$\begin{aligned} & \Rightarrow 2 \pi r=\frac{44 a}{10} \\ & \Rightarrow r=\frac{44 a}{2 \pi \times 10} \\ & \Rightarrow r=\frac{11 a}{5 \pi} \\ & \Rightarrow a=\frac{5 \pi r}{11} \end{aligned}$$ Also, $\pi r^{2}-a^{2}=216$