Question

In fig. 9.34, seg AB and seg CD are perpendicular diameter of a circle with radius 7 cm. seg AO is the diameter of smaller circle. Find the area of shaded region.

Answer 1

Radius of the bigger circle = OC = 7 cm
Diameter of the smaller circle = radius of the bigger circle = 7 cm
Radius of the smaller circle = $\frac{7}{2}$ cm = 3.5 cm
Area of the smaller circle = $\pi (3.5{)}^2=\frac{22}{7}\times 3.5\times 3.5=38.5{\mathrm{cm}}^2$
Area of the bigger semicircle = $\frac{\pi (7{)}^2}{2}=\frac{{\displaystyle \frac{22}{7}}\times 7\times 7}{2}=77{\mathrm{cm}}^2$
i.e., OC = OB = 7 cm
or CD = 2 OC = 14 cm

It is given that AB and CD are perpendicular bisectors.
Then area of the $△$BCD = $\frac{1}{2}\times \mathrm{CD}\times \mathrm{OB}=\frac{1}{2}\times 14\times 7{\mathrm{cm}}^2=49{\mathrm{cm}}^2$
$\therefore$ Area of the shaded region = area of the smaller circle + area of the bigger semi circle − area of the $△$BCD
= (38.5 + 77 – 49) cm²
= 66.5 cm²