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

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.

Area of circle = pi * radius^2radius is given to be 1/2 inchespi * (1/2)^2 = pi/4 inches^2 = 0.785 inches^2