passwella.
Menu

WAEC Mathematics 1991 (August) Question 48

Question 48

Mensuration of Plane Shapes

In the diagram below, PQ and XY are two concentric arcs; centre O. If the ratio of the lengths of the two arcs is 1 : 3, find the ratio of the areas of the two sectors OPQ and OXY.

Diagram for this question
  1. A.1 : 3
  2. B.1 : 6
  3. C.1 : 9
  4. D.2 : 3
  5. E.4 : 9
Show the answer and explanation

Answer: C (1 : 9)

Explanation

Both sectors have the same angle, so the arc lengths are in the ratio of the radii, 1 : 3. Areas go as the square of the radius: 1 : 9.