Question

Four identical coins are placed in a square. For each coin, the ratio of area to circumference is the same as the ratio of circumference to area. Find the area of the square that is not covered by the circle?

• 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 the given condition,

$\frac{\pi R^2}{2\pi R}=\frac{2\pi R}{\pi R^2}$

$\Rightarrow \frac{R}{2}=\frac{2}{R}$

$\Rightarrow R^2=4$

$\Rightarrow R=2$

$\therefore$ length of the side of the square $4R=8$ units.

Area which is not covered by coins $=8\times 8-4\times \pi {\left(2\right)}^2=64-16\pi =16(4-\pi )$.