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JAMB Mathematics 1985 Question 47

Question 47

Mensuration of Plane Shapes

In the figure above the area of the shaded segment is

Diagram for this question
  1. A.3π
  2. B.9√3/4
  3. C.3(π − 3√3/4)
  4. D.3(√3 − π)/4
  5. E.π + 9√3/4
Show the answer and explanation

Answer: C (3(π − 3√3/4))

Explanation

Sector = 120/360 × π × 3² = 3π. Triangle = ½ × 3 × 3 × sin 120° = 9√3/4. Segment = 3π − 9√3/4 = 3(π − 3√3/4).