The diagram above shows the shaded segment of a circle of radius 7cm. if the area of the triangle OXY is 12\(\frac{1}{4}\)cm\(^2\), calculate the area of the segment
[Take \pi = 22/7]
Attached Figure / Diagram
A
5/12cm2
B
7/12cm2
C
11/6cm2
D
2 1/3cm2
E
6 1/6cm2
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Area of \(\Delta OXY\) = \(12\frac{1}{4} cm^2\)
Area of sector OXY = \(\frac{30}{360} \times \frac{22}{7} \times 7 \times 7\)
= \(\frac{77}{6} = 12\frac{5}{6} cm^2\)
Area of the shaded portion = \(12\frac{5}{6} - 12\frac{1}{4}\)
= \(\frac{7}{12} cm^2\)
Source: Myschool Past Questions Archive (Record #23156)