Question

$PQRS$ is the diameter of a circle of radius $6cm$. The length $PQ,QR$ and $RS$ are equal. Semi-circle is drawn with $PQ$ and $QS$ as diameters as shown in the figure. The ratio of the area of the shaded region to that of the unshaded region is

• A. $3:5$
• B. $5:3$
• C. $3:4$
• D. $5:2$

Answer 1

The correct option is A $3:5$

The ratio of area of shaded region to that of the unshaded region

= (area of bigger semicircle-area of smaller semicircle) / (area of bigger semicircle+area of smaller semicircle)

$=\frac{\frac{\pi R^2}{2}-\frac{\pi r^2}{2}}{\frac{\pi R^2}{2}+\frac{\pi r^2}{2}}$

$=\frac{R^2-r^2}{R^2+r^2}$

$=\frac{(2r{)}^2-r^2}{(2r{)}^2+r^2}$

$=\frac{3}{5}$