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 one decimal place, the length of arc PQ.
To calculate the length of an arc, we can use the formula:
Arc length = (θ/360) * 2πr
Where:
- θ is the central angle in degrees
- r is the radius of the circle
- π is approximately 3.142
In this case:
- θ = 50°
- r = 3.5 cm
So, the arc length PQ = (50/360) * 2 * 3.142 * 3.5
Arc length PQ = (50/360) * 21.994
Arc length PQ = 0.13888 * 21.994
Arc length PQ = 3.054 cm
Rounding to one decimal place, the length of arc PQ is approximately 3.1 cm. However, since 3.1 is not an option, there might be a calculation error or a mistake in the provided options. Recalculating the formula: Arc length = (50/360) * 2 * 3.142 * 3.5 = 3.054 Rounding to one decimal place, arc length = 3.1 cm None of the options have the correct answer.
Based on the provided options, let's review each option again to see if a calculation was made. A. 175.0cm: Incorrect B. 157.1cm: Incorrect C. 37.7cm: Incorrect D. 11.0cm: This appears to have been calculated using (50/360) * 2 * 3.142 * 3.5 * 2 = 6.1 which could be the arc length of 2 arcs combined. Still, the correct arc length is not amongst the options.
Recalculating: (50/360) * 2 * 3.142 * 3.5 = 3.054 There must be a calculation error or misprint, 11.0cm is incorrect.
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