OK, I'm teaching myself calculus and the book I'm using wasn't particularly clear on this, so I'll give you the problem, the solution, and the part I don't comprehend...
[b]A sponge is in the shape of a right circular cone. As it soaks up the water, it grows in size. At a certain moment, the height equals 6 inches, and is increasing at the rate of .3 inches per second. At that same moment, the radius is 4 inches, and is increasing at the rate of .2 inches per second. How is the volume changing at that time?
So, height = 6 in and is increasing by .3 in/sec
Radius is 4 inches and is increasing by .2 in/sec
The volume of a right circular cone is (If someone could tell me how to write the symbol for pi in the [ Tex ] tags, that'd be helpful in the future.)
Now is where I get confused, to derive that formula in respect to the variable t which is time. As well, I was unsure of how to apply the product rule when I have three different numbers being multiplied at once...
The book gives this;
I realize that is the rate the radius is increasing and is the rate the height is increasing, but knowing when/ where/ why to use them is what I don't get.
I think someone may just need to explain each step in the problem and I'll get it.