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JAMB Mathematics 2000 Question 37

Question 37

Integration

A bowl is designed by revolving completely the area enclosed by y = x2 − 1, y = 0, y = 3 and x ≥ 0 around the y-axis. What is the volume of this bowl?

  1. A.7π cubic units
  2. B.15π/2 cubic units
  3. C.8π cubic units
  4. D.17π/2 cubic units
Show the answer and explanation

Answer: B (15π/2 cubic units)

Explanation

Around the y-axis, V = π∫x2 dy with x2 = y + 1. From y = 0 to 3 this is π[y2/2 + y] = π(4.5 + 3) = 15π/2.