Question

A spherical balloon is being inflated so that, at the time when the radius is 5m, the radius is increasing at the rate of 0.15m/s.

(A) Find the rate of increase of the volume at this time.
(B) If the rate of increase of volume thereafter remains constant, find the rate at which the radius is increasing when the balloon has a diameter of 12m.

Please help, totally lost.

Answer 1

There are two ways of thinking about this:

1. Straight math
V = (4/3) pi r^3
dV/dr = 4 pi r^2

2. Common sense
dV = surface area * dr
dV = 4 pi r^2 dr

anyway
dV/dt = dV/dr dr/dt
dV/dt = 4 pi (25) (.15)

if D = 12 then r = 6
dr = dV/4 pi r^2
dr/dt = (1/4*36 pi ) dV/dt