Find the rate of change of the surface area of a sphere with respect to the radius r. what is the rate when r = 6?

48pi which is approximately 150.7964 The formula for the area of the surface of a sphere is 4pi r^2. The first derivative of that equation will give the rate of change of the surface area. So multiply the constant by the exponent and then subtract one from the exponent. So the first derivative of 4pi r^2 is 8pi r The rate when r = 6 is then calculated by substituting 6 for r in the expression. 8pi 6 = 48pi which is approximately 150.7964