Question on: WAEC Mathematics - 1998
In the diagram O is the center of circle PRQ. The radius is 3.5cm and ∠POQ = 50o. Use the diagram to answer question below. (take π = 3.142)
Calculate, correct to three significant figures, the area of sector OPQ
Calculate, correct to three significant figures, the area of sector OPQ
A
3.403cm2
B
5.350cm2
C
10.99cm2
D
157.1cm2
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Correct Option: B
To calculate the area of sector OPQ, we can use the following steps:
1. **Formula:** The area of a sector is given by the formula:
Area = (θ/360) \* πr²
where θ is the angle of the sector in degrees, and r is the radius of the circle.
2. **Identify Values:**
* θ = 50°
* r = 3.5 cm
* π = 3.142
3. **Substitute and Calculate:**
Area = (50/360) \* 3.142 \* (3.5)²
Area = (50/360) \* 3.142 \* 12.25
Area ≈ 0.138888 \* 38.485
Area ≈ 5.345 cm²
4. **Round to Three Significant Figures:** The area of the sector OPQ is approximately 5.35 cm².
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