Question

The volume of a conical pile of sand is increasing at a rate of 243π ft3/min, and the height of the pile always equals the radius r of the base. Express r as a function of time t (in minutes), assuming that r = 0 when t = 0.

Answer 1

Volume = 1/3 π r^2 h

given the height = radius

Volume = 1/3 π r^3

. . . Volume = 243 π * t .. in cubic feet

243 π t = 1/3 π r^3

r^3 = 729 * t

r = 9 t^(1/3) feet