Final answer:
The instantaneous rate of change of the volume V with respect to the radius r, for the formula V = 4/3(pi)r³, is found using differentiation, resulting in dV/dr = 4(pi)r².
Step-by-step explanation:
To find the formula for the instantaneous rate of change of the volume V with respect to the radius r, given that V = ⅔(π)r³, we need to use differentiation. Differentiating both sides of the equation with respect to r, we get:
dV/dr = 4(π)r²This formula represents the instantaneous rate of change of the volume with respect to the radius, which can also be interpreted as how much the volume changes for a small change in radius.