A sump pump is dumping sand into a pile at a rate of 6 cubic feet per second, forming the shape of a cone. If the cone always grows such that the height is three times the radius, find the rate of change of the height of the pile of sand at the point when the height is 12 feet.|||Zero. Pumped sand slurry has an extremely high angle of repose and will not form a cone like that. Now if the cone is something else - - H is the 12 ft, h is the new height V =1/ 3 *Pi *R^2 *H In your case V= 1/3 * Pi * (H/3)^2* H Where H is 12, V = Pi/3 * H^3 /9 , V= Pi/3 * 12^3 /9 = 201 Add 6 cu ft : 207 = Pi/3 *h^3 /9 , h^3 = 207* 27/ Pi h = 1779^-3 = 12.12 ft, the new height The rate is 0.12 ft per sec.

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