A water tank in the shape of a cone is being filled at a constant rate. The volume of water in the tank at time $t$ is given by the equation $V(t) = \frac{1}{3}\pi r^2h$, where $r$ is the radius of the base of the cone and $h$ is the height of the water in the cone. The radius of the base of the cone is increasing at a rate of 0.5 meters per minute, and the height of the water in the cone is increasing at a rate of 2 meters per minute. If the initial radius of the base of the cone is 1 meter and the initial height of the water in the cone is 2 meters, what is the rate at which the volume of water in the tank is increasing at time $t = 5$ minutes?
Mathbot Says...
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