Question

A water tank is in the shape of an inverted cone with depth 10 meters and top radius 8 meters. water is flowing into the tank at 0.6 cubic meters/min but leaking out at a rate of 0.001h^2 cubic meters/min, where h is the depth of the water in meters. can the tank ever overflow?

Answer 1

To determine if the water tank will overflow, calculate the rate of water flow into the tank and compare it to the rate of water flow out of the tank.

Step-by-step explanation:

This problem can be solved by finding the rate of water flow into the tank and comparing it to the rate of water flow out of the tank.

Given that water is flowing into the tank at a rate of 0.6 cubic meters/min and leaking out at a rate of 0.001h^2 cubic meters/min, we need to determine if the tank will ever overflow.

We can calculate the rate of water flow out of the tank by substituting the given depth of the water, 10 meters, into the equation. If the rate of water flow out of the tank is greater than the rate of water flow into the tank, then the tank will not overflow.

By calculating the rate of water flow out of the tank using the given depth, we can determine whether the tank will overflow or not.