I am new to this forum so I hope i post this question at the right level.
A spherical vacuole (something in a cell) is decreasing in size so that its volume decreases at a constant rate of 100 cubic micrometres per seconds. At what rate is the radius decreasing at the instant when the radius of 5 micrometre.
This question needs the chain rule and is based on related rates of change.
So, the [change in the radius wrt time] is equal to the [change in the radius wrt to the volume] * [change in the volume wrt time]
dr /dt = dr/dv * dv/dt
The change in volume wrt time is constant at 100, so can substitute dv/dt for 100 (or -100 because its a decrease?)