Question

If the radius of a sphere is increasing at the rate of 2 inches per second how fast

Answer 1

You haven't shared all of the question, so I'll guess that you want to find "how fast is the area of the sphere increasing?"

Area of a sphere = 4*pi*r^2

Rate of change of area of a sphere with respect to radius r:

               dA/dr = 8*pi*r*(dr/dt)

Here, that would come out to    

           dA/dr = 8*pi*r*(2 inches / sec)


If you meant, "how fast is the volume of the sphere increasing?" you'd need to use a different equation:


V = (4/3)*pi)*r^3

and go through a similar process.