Mathematics 2019 JAMB Past Questions - Question 5: 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 0cm3, find the volume of the balloon after 2 seconds.

Correct Answer

B

Explanation

To find the volume of the balloon after 2 seconds, we can integrate the given rate of change of volume with respect to time.The rate of change of volume is given as π(20 - t^2) cm^3 s^-1. To find the volume after 2 seconds, we integrate this expression with respect to t from 0 to 2:∫[0 to 2] π(20 - t^2) dtThis integration will give us the total change in volume from t = 0 to t = 2 seconds.Evaluating the integral:∫[0 to 2] π(20 - t^2) dt = π[20t - (t^3)/3] evaluated from 0 to 2                          = π[40 - (8/3)]                          = π(120/3 - 8/3)                          = π(112/3)                          = 112π/3 cm^3So, the volume of the balloon after 2 seconds is 112π/3 cm^3.To find the volume of the balloon after 2 seconds, we can integrate the given rate of change of volume with respect to time.The rate of change of volume is given as π(20 - t^2) cm^3 s^-1. To find the volume after 2 seconds, we integrate the rate of change of volume with respect to time from 0 to 2 seconds:∫[0 to 2] π(20 - t^2) dtEvaluating this integral gives us the change in volume over the interval [0, 2]. Adding this change to the initial volume of 0 cm^3 gives us the volume of the balloon after 2 seconds.