Everything challenging in Math can be solved by following a simple procedure:
1. For 2 unit, memorise the formulas.
2. Read the examples in text-book thoroughly. Your teacher should go through these examples with you in class.
3. Tackle any questions you can do in the text book first. Skip the ones you cannot do and circle it, wait for an opportunity to ask your teacher, whether after class or during your own time. Make sure for this topic you write out EVERYTHING you know - it made it simpler for me.
4. Redo the questions you do not understand yourself.
5. Repetition helps a lot in math.
In rates of change, it is generally:
rate of change of volume or surface area = differentiation of the volume or surface area of the shape x rate of change of radius or height.
You'll need to know your volume and surface area formulas.
(^ sorry if the above wording is terrible).
EDIT:
For example, I'll make up a random question on the spot:
The radius of the volume of a sphere is constantly increasing at 2 cm/s. Given that the radius was initially 5 cm, Find the rate of change of the volume of the sphere.
Here, we know that we must use:
dv/dt = dv/dr * dr/dt
(they are equal since dr cancels out with each other)
dv/dt is the rate of change of volume (v) in time (t).
dv/dr is the derivative of the volume (v) with respect to the radius (r).
dr/dt is the rate of change of the radius (r) in time (t).
we are given that the radius is constantly increasing at 2 cm/s
So, dr/dt = 2
We know that the volume of a sphere is calculated by: V = 4/3πr³
so dv/dr = (4/3πr³)' = 4πr²
therefore,
dv/dt = dv/dr * dr/dt
dv/dt = 4π(5)² * 2
dv/dt = 200π cm³/s
hopefully that run-through helps you with majority of the rates of change problems.
also note that in these questions, they MAY ask you to find the rate of change of the radius or height or whatever. It's basically the same procedure, and they will give you the rate of change of the volume or surface area.
