Suppose there are all these bubbles, where each bubble is shaped as a different type of surface. One of the bubbles is shaped as a circular cylinder, and it will keep that general shape over time, although the height increases at a rate of 3 cm/sec while the radius will decrease at a rate of 1 cm/sec (and when the bubble gets thin enough it will eventually pop).
1.) What rate is the volume, V, of this bubble changing when it is 10 cm high and 6 cm across at the bottom?
2.) What rate is the surface area of the bubble changing at the same instant?
So using the info. given, it would be:
Pi*2*3*10*1 + Pi*3^2*3 = 60*Pi + 27*Pi = 87*Pi and so it is changing at a rate of 87*Pi cm/sec ?
I have the 3 in bold since when the prob. says "6 cm across" I assume it means the diameter, and therefore the radius is 3.