Final answer:
The rate of change of the volume of a cone with respect to time is calculated by differentiating the volume formula and substituting the given rates of change for the radius and height.
Step-by-step explanation:
The question at hand involves calculus, specifically related to the rate of change of the volume of a cone with respect to time. To solve this, one would use the given formula for the volume V of a cone, which is V = (1/3)πr^2h, and apply the chain rule to differentiate both sides with respect to time (t).
The rate of change of the volume with respect to time, represented as dV/dt, can be found by differentiating the volume formula:
dV/dt = πr^2(dh/dt)/3 + 2πrh(dr/dt)/3
This formula incorporates the given rates of change of both the radius (dr/dt, in litchis per minute) and the height (dh/dt, in units per minute) to find the final rate at which the volume changes over time.