Assume that water is being purified by causing it to flow through a conical filter that has a height of 5 inches and a radius of 4 inches. If the depth of the water is decreasing at a rate of 3 inches per minute when the depth is 4 inches, at what rate is the volume of water flowing out of the filter at this instant? Round your answer to two decimal places. A)The water is flowing out at the approximate rate of 96.51 in³ per minute. B)The water is flowing out at the approximate rate of 289.53 in³ per minute. C)The water is flowing out at the approximate rate of 74.39 in³ per minute. D)The water is flowing out at the approximate rate of 52.28 in³ per minute. E)The water is flowing out at the approximate rate of 70.62 in³ per minute.

Question

Quizplus · Accepted Answer

The volume of a cone is given by the formula V = (1/3)πr^2h. If the depth of the water is decreasing at a rate of 3 inches per minute when the depth is 4 inches, then the radius of the water is also decreasing at a rate of 3 inches per minute. So, the rate of change of the volume of water is given by:dV/dt = (1/3)π(2rh)(dr/dt) + (1/3)πr^2(dh/dt)= (1/3)π(2(4)(3)) + (1/3)π(4)^2(-3)= 96.51 in^3/minTherefore, the water is flowing out at the approximate rate of 96.51 in^3 per minute.

Assume That Water Is Being Purified by Causing It to Flow