A spherical balloon is being inflated and the radius of the balloon is increasing at a rate of 2 cm/s.

Question

A spherical balloon is being inflated and the radius of the balloon is increasing at a rate of 2 cm/s.

(a) Express the radius r of the balloon as a function of the time t (in seconds).

(b) If V is the volume of the balloon as a function of the radius, find V o r and interpret it.

Answer 1

Volume of a sphere = V(r) = (4/3)πr³

Given: dr/dt = 2 cm/s

a) r(t) = 2 t

b) (V o r)(t) = V(r(t)) = (4/3)π(2t)³ = (32/3)πt³

This is the volume of the balloon as a function of time, V(t).