Find the change in height of a cone being filled with water, related rates

The video tutorial explains how to calculate the rate at which the water level rises in a right circular cone. It begins with the volume formula for a cone and discusses the need for derivatives to find rates of change. The problem is complicated by unknown variables, leading to the creation of a relationship between the radius and height. This relationship simplifies the equation, allowing for easier differentiation and solving for the rate of change of height.

What challenges arise when trying to find the rate of change of height with insufficient information?

What is the final expression for the volume in terms of height?

What relationships can be used to find the radius when the height is known?

Why is it important to consider the units when calculating the rate of change of height?