Question

In the figure shown, a semicircle $BQCPA$ is drawn on the diameter $AOB$, with $OA=OB=OC=7\text{cm}$. Find
(i) The area of the sector $CPAO$
(ii) The area of the segment $CPA$
(iii) The area of shaded region.

• A. (i) 38 (i) 14 (iii) 28
• B. (i) 38.5 (i) 14 (iii) 28
• C. (i) 38 (i) 14.5 (iii) 28
• D. (i) 38 (i) 14 (iii) 28.5

Answer 1

The correct option is B (i) 38.5 (i) 14 (iii) 28



(i) The area of sector $CPAO$:
$\frac{\theta }{{360}^{\circ }}\times \pi r^2$
$=\frac{{90}^{\circ }}{{360}^{\circ }}\times \frac{22}{7}\times 7\times 7$
$=\frac{77}{2}$
$=38.5{\text{cm}}^2$

(ii) The area of segment $CPA$:
$=38.5{\text{cm}}^2-\frac{1}{2}\times 7\times 7$
$=38.5-\frac{49}{2}=38.5-24.5$
$=14{\text{cm}}^2$

(iii) The area of shaded region:
$=$ Area of segment $CPA+$ Area of segment $CQB$
$=2$ (Area of segment $CPA$)
$=2\left(14\right)$
$=28{\text{cm}}^2$