I need help understanding the steps to solving these problems:
1. A spherical balloon is expanding. If the radius is increasing at the rate of 2 inches per minute, at what rate is the volume increasing when the radius is 5 inches?
I know to start off, I have to take the derivative of V, which is 4piR^2 * dr/dt, which equals dr/dt=dV/dt/(4piR^2). I'm stuck after that.
2. A particle moves in a circular orbit x^2 + y^2 = 16. As it passes through the point (2, 2sqrt(3)), its y-coordinate decreases at a rate of 3 units per second. At what rate is the x-coordinate changing?
3. A triangle, whose h = 2b, has an area A = 1/2bh=1/2b(2b)=b^2 is expanding with time. If dA/dt = 8 cm2/s, what is db/dt when b = 2?
4. A heap of garbage in the shape of a cube is being compacted. Given that the volume decreases at a rate of 2 cubic meters per minute, find the rate of change of an edge of the cube when the volume is exactly 27 cubic meters.
There are a lot more, but I think if I knew how to do these, I could figure out the others.