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JAMB Mathematics 1980 Question 28

Question 28

Mensuration of Plane Shapes

In the figure above, FGHJ is a circle of radius 3cm centre O. FOH, GOJ are perpendicular diameters. With G as centre, an arc of a circle is drawn to pass through F and H. Find the length of the perimeter of the lunar portion shaded.

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

Answer: B (3π(1 + √2/2) cm)

Explanation

The outer edge is half the small circle: π × 3 = 3π. The inner edge is an arc of radius GF = 3√2 subtending 90° at G: ¼ × 2π × 3√2 = 3√2π/2. Total 3π(1 + √2/2)cm.