Question

a recreational lake created by an artificial damn has the shape of a truncated cone. if the depth of water in the lake (h) is 0 the radius of the lake would be r_1= 300meters. the radius of the lake at it's surface is given in terms of the lake's depth via the following relation r_2 = 300 + h.

a) given that the volume of a truncated cone is given by the formula pi/3 × h(r(2/1)+ r(2/2) + r _1×r_2) find a formula for the volume of the water behind the damn in terms of the height of the water.
b) to minimize the build up of sediment once a year the flood gates are opened allowing water from the lake to flood down the river. after 1 hour the engineer notices the lake is now only 200 meters deep and the depth is decreasing at a rate of 1.2 meters/hour. calculate the rate (in cubic meters/hour)at which water is flowing out of the flood gate sand determine if the engineer is going to be fired for letting the water flow downstream at more than a million cubic meters per hour.

Answer 1