A tank is in the shape of a right circular cone with top radius 2 m and height 5 m. It contains water up to the height of 4 m. The density of water is 1,000 kg/m³. How much work must be done to pump all of the water out of the tank over the top edge of the tank? A) 21,447 kg . m B) 20,210 kg . m C) 23,556 kg . m D) 23,879 kg . m E) 210,177 kg . m

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Quizplus · Accepted Answer

The work done is equal to the weight of the water, which is equal to the density of water times the volume of water times the height to which the water is lifted. The volume of water is equal to the volume of the cone, which is given by the formula V = (1/3)πr^2h, where r is the radius of the base of the cone and h is the height of the cone. The height to which the water is lifted is equal to the height of the cone minus the height of the water in the cone. Therefore, the work done is equal to:W = ρVg = (1,000 kg/m^3)(1/3)π(2 m)^2(5 m - 4 m) = 21,447 kg . m

A Tank Is in the Shape of a Right Circular