Acoffee filter in the shape of an inverted cone (8 inches in diameter and 4 inches tall) is dripping coffee. there is a cylindrical coffee pot (10 inches in diameter and 6 inches tall) below the cone. how fast is the height of the coffee in the pot increasing when the level of coffee in the filter is 2 inches and decreasing at a rate of .2 inches per second?

0.032 inches per second

Explanation:

The volume of the conic filter is given by:

The relation between the height and radius is:

R = (8inches/2)/4inches*h

R = h   Replacing this:

The derivative of the volume is:

The decreasing rate change on the filter's volume is the same increasing change rate on the coffee pot's volume. Since the volume of the pot is:

The derivative is:

  where h' is the change rate in its height:

h' = 0.032 inches/s

that would be because of both gravity and friction. so     c

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