Question

$PQRS$ is a square, $4$ equal circles are just touching each other whose centres are the vertices $P,Q,RandS$ of the square. What is the ratio of the shaded to the unshaded area within square ?

• A. $\frac{8}{11}$
• B. $\frac{3}{11}$
• C. $\frac{5}{11}$
• D. $\frac{6}{11}$

Answer 1

Answer: (B)

$\frac{3}{11}$

Lets us take radius of the square= x
So, side of square=2x
unshaded area within square=
$A=4\ast \frac{1}{4}\ast \Pi r^2$
$A=\Pi r^2=\frac{22}{7}{x}^2$
shaded area within square=
$A=a\ast a-\Pi r^2={2x}^2-\frac{22}{7}{x}^2=\frac{6}{7}{x}^2$
$Ratio=\frac{shadedareawithinsquare}{unshadedareawithinsquare}=\frac{\frac{6}{7}{x}^2}{\frac{22}{7}{x}^2}=\frac{3}{11}$
Answer (B) $\frac{3}{11}$