Question

water is leaking out of an inverted conical tank at a rate of 0.0111 m3/min. at the same time water is being pumped into the tank at a constant rate. the tank has height 13 meters and the diameter at the top is 3.5 meters. if the water level is rising at a rate of 0.2 m/min when the height of the water is 4 meters, find the rate at which water is being pumped into the tank.

Answer 1

To find the rate at which water is being pumped into the tank, use the volume equation for a cone. Set up a proportion to find the rate of water pumped using the given information. The rate at which water is being pumped into the tank is approximately 0.001287 m³/min.

Step-by-step explanation:

To find the rate at which water is being pumped into the tank, we need to use the volume equation for a cone. The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height. We know that the diameter at the top of the tank is 3.5 meters, so the radius is half of that, which is 1.75 meters. The height of the tank is given as 13 meters. We also know that the water level is rising at a rate of 0.2 m/min when the height of the water is 4 meters.

First, let's find the volume of the tank when the water level is at 4 meters:

V = (1/3)π(1.75)^2(4) = 16.333 m^3

The rate at which the volume is increasing is 0.2 m/min, so we can set up a proportion to find the rate at which water is being pumped into the tank:

(0.2 m/min)/(16.333 m^3) = (x m/min)/(0.0111 m^3)

Solving for x, we get x ≈ 0.001287 m/min.

Therefore, the rate at which water is being pumped into the tank is approximately 0.001287 m³/min.