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. The area of the square not covered by the coins is

• 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 the radius of each coin$=r$.
Then, $\frac{\pi r^2}{2\pi r}=\frac{2\pi r}{\pi r^2}$

$\Rightarrow r^2=4$

$\Rightarrow r=2$
$\therefore$ Each side of the square $=4\times 2cm=8cm$
$\therefore$ Area of the square not covered by coins $=$ Area of square $-$ Area covered by 4 coins
$=64-4\times \pi \times (2{)}^2$

$=64-16\pi$

$=16(4-\pi )$