The area of a sector of a circle with radius 7cm is 51.3 cm\(^2\). Calculate, correct to the nearest whole number, the angle of the sector. (Take \(\pi\) = \(\frac{22}{7}\))
A
60\(^0\)
B
120\(^0\)
C
150\(^0\)
D
150\(^0\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Area of a sector = \(\frac{\theta}{360}\) x \(\pi\) r\(^2\)
51.3 = \(\frac{\theta}{360}\) x \(\frac{22}{7}\) x 7 x 7
\(\theta\) = \(\frac{51.3 \times 360}{22 \times 7}\) = 119.9 ≈ 120º to the nearest whole number.
Source: Myschool Past Questions Archive (Record #71859)