Question

Four identical coins are placed in a square. For each coin, the ratio of area to circumference is same as the ratio of circumference to area.

Then, find the area of the square that is not covered by the coins

• A. $16(\pi -1)$
• B. $16(8-\pi )$
• C. $16(4-\pi )$
• D. $16(4-\frac{\pi }{2})$

Answer 1

The correct option is C $16(4-\pi )$

Let r be the radius of each circle.
Then by given condition,
$\frac{\pi R^2}{2\pi R}=\frac{2\pi R}{\pi R^2}\Rightarrow R^2=4\Rightarrow R=2$
$\therefore$ The length of the side of the square = 8
Now the area covered by 4 coins $=4\times \pi (2{)}^2=16\pi$
and area of the square = 64
$\therefore$ The area which is not covered by the coins
= 64 - $16\pi$ = 16 (4 - $\pi$)