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JAMB Mathematics 1992 Question 40

Question 40

Integration

A student blows a balloon and its volume increases at a rate of π(20 − t2)cm3 s−1 after t seconds. If the initial volume is 0 cm3, find the volume of the balloon after 2 seconds.

  1. A.37.00π
  2. B.37.33π
  3. C.40.00π
  4. D.42.67π
Show the answer and explanation

Answer: B (37.33π)

Explanation

V = π(20t − t3/3), starting from 0. At t = 2: π(40 − 8/3) = 37.33π.