Question on: WAEC Mathematics - 1998

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.