Help with my hw :(

[raDixGhost]

Well this is my last resort i dont know how to do this problem.

What is the rate of change of the volume of a sphere with respect to the radius when the radius is r = 2 in?

I have no idea how to do that. I think it wants a limit and find its tangent's slope. But i have no idea how to abract that idea or where to start.

 

[x42bn6]

Well: this is how I would do it.

Note: * = times, ^ = power of

V=4/3*pi*r^3
r=2in
We want dV/dt.
dV/dt=dV/dr*dr/dt
dV/dr=4*pi*r^2
dV/dr when r=2in=4*pi*2^2=16*pi
dV/dt=dV/dr*dr/dt
dV/dt=16*pi*dr/dt

However, one gaping mistake: you have not given the rate of change of the radius.

Remember, |y=dy/dx*|x where | is delta.*