WAEC 2020 Mathematics · Question 17

The length of an arc of a circle of radius 3.5 cm is 1 19/36 cm. Calculate, correct to the nearest degree…

Question

The length of an arc of a circle of radius 3.5 cm is 1 $\frac{19}{36}$ cm. Calculate, correct to the nearest degree , the angle substended by the centre of the circle. [Take $\pi = \frac{22}{7}$ ]

A.55 $^o$
B.36 $^o$
C.25 $^o$
D.22 $^o$

Answer: C. 25 $^o$

Explanation written with AI and checked against the answer key

Analyze the question: We are given an arc length and the radius, and we must find the angle at the centre (in degrees). Concept: Arc length = (θ/360) × 2πr Solution: Arc length = 1 19/36 = 55/36 cm 2πr = 2 × (22/7) × 3.5 = 2 × 22 × 0.5 = 22 cm So: θ/360 = (55/36) ÷ 22 = 55/(36 × 22) = 5/72 θ = (5/72) × 360 = 25° Answer: The angle is exactly 25°, so the nearest degree is 25°. Tip: Simplify 2πr first. With r = 3.5 and π = 22/7, the 7 cancels neatly and the circumference is 22 cm. Convert mixed numbers to improper fractions before dividing (1 19/36 = 55/36).

AI can make mistakes. Report anything that looks wrong.

The length of an arc of a circle of radius 3.5 cm is 1 19/36 cm. Calculate, correct to the nearest degree…

Question

Answer: C. 25o^oo

Answer: C. 25 $^o$