Filtering water Suppose 5 in3 of water is poured into a conical filter and subsequently dr...

Filtering water Suppose 5 in3 of water is poured into a conical filter and subsequently drips into a cup, as shown in the figure. Let x denote the height of the water in the filter, and let y denote the height of the water in the cup.

(a) Express the radius r shown in the figure as a function of x. (Hint: Use similar triangles.)

(b) Express the height y of the water in the cup as a function of x. (Hint: What is the sum of the two volumes shown in the figure?)

EXERCISE