Question

a conical water tank has a top radius of 20 meters and a depth of 20 meters. water is being pumped into the tank at the rate of 40 cubic meters per minute. how fast is the level of the water rising when the water is 8 meters deep?

Answer 1

To find how fast the level of the water is rising in a conical water tank, use the formula for the volume of a cone and differentiate it implicitly with respect to time. The rate at which the level of the water is rising when the water is 8 meters deep is approximately 0.251 meters per minute.

Step-by-step explanation:

To find how fast the level of the water is rising, we can use the formula for the volume of a cone, which is V = (1/3)πr^2h, where r is the radius of the top of the cone and h is the height of the cone. We can differentiate this equation implicitly with respect to time to find the rate of change of the volume with respect to time.

Since we are given the rate of change of volume, which is 40 cubic meters per minute, we can use the chain rule to find the rate of change of the height, dh/dt.

Using the given values, we can substitute in the values for r and h when the water is 8 meters deep, and solve for dh/dt.

After simplifying the equation and evaluating the values, we find that the rate at which the level of the water is rising when the water is 8 meters deep is approximately 0.251 meters per minute.