True or False question: If the radius of a sphere is increasing at 3 ft/sec,volume increasing @27cubicft/sec?

Let R = radius


V = volume


t = time





V = 4/3 * pi * R^3


dV/dt = 4/3 * pi * 3R^2 * dR/dt


dV/dt = 4 * pi * R^2 * dR/dt


dR/dt = 3 ft/s


dV/dt = 4 * pi * R^2 * 3 = 12 * pi * R^2





As you can see, you need to know the current value of radius (R).


But if what you have typed is the complete question, then the answer is False.


This is because when such questions are given, what it means is that when radius is increasing at 3 ft/s, then volume will ALWAYS increase at 27 cubic ft/s. But we know that this is not true.True or False question: If the radius of a sphere is increasing at 3 ft/sec,volume increasing @27cubicft/sec?
Not enough information, but probably false.





You would need to know the size of the radius at the instant it is increasing at 3 f/s to say for sure.True or False question: If the radius of a sphere is increasing at 3 ft/sec,volume increasing @27cubicft/sec?
Your not given enough information to tell for sure, but it is most likely going to be false. If this is a test question i would put false and hope for the best. Did you type the entire question? o.O
volume of sphere = 4/3 pi r3


lets say r=1 at t=0


r=4 at t=1


r=7 at t=2


if you apply above formula, you will see volume doesnt increase at a rate of 27 cubft/sec each second