Question

A balloon is inflated so that its increase in volume is at a constant rate of 10cm^3 s^-1. If its volume is initially 1 cm^3, find its volume after 3 seconds.

Answer: 31 cm^3

Answer 1

Rate of increase:

dV / dt = 10

dV = 10 dt

Integrating both sides:

V = 10 t + C

C = integration constant

Initial condition:

t = 0 , V = 1

V = 10 t + C

1 = 10 ∙ 0 + C

1 = 0 + C

1 = C

C = 1

V = 10 t + C

V = 10 t + 1

After 3 seconds:

V = 10 ∙ 3 + 1

V = 31 cm³