Average rate of change is just the slope of the secant line. Plug in 25cm and 20cm for both equations to get the y-values that go with them. Then just use y2-y1/x2-x1 to get the slope. That's your average change.
i.e. 4πr^2 yeilds the coordinates (25, 4π(25)^2) and (20, 4π(20)^2). So, your answer is [4π(25)^2 - 4π(20)^2]/(25-20)
For instantaneous change at 10cm, just derive both equations with respect to x and plug in 10cm for x.
i.e. for (4/3)πr3, our derivative is surface area 4πr^2. Plug in for 10cm, and you get your answer.