WAEC Mathematics 1988 Question 42

Question 42

Mensuration of Plane Shapes

A rope of length 18m is used to form a sector of a circle of radius 3.5m, on a school playing field. What is the size of the angle of the sector, correct to the nearest degree?

A.33°
B.40°
C.90°
D.180°
E.270°

Show the answer and explanation

Answer: D (180°)

Explanation

The rope forms two radii and the arc: arc = 18 − 2(3.5) = 11 m. The full circumference is 2 × 22/7 × 3.5 = 22 m, so the angle = 11/22 × 360° = 180°.