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Grain pouring from a conveyor belt falls into a pile in the shape of a cone. The grain is falling at a rate of and forms a pile such that the radius is always half the height. How fast is the height of the pile increasing when the radius is meters?

Sketch the cone, and label the sides of similar right triangles that are formed by its radius and height.

Write a geometric equation describing the volume of the cone in terms of height.
You will have to find a way to define in terms of .
Since the radius changes as the height changes, do NOT 'plug in' any values yet.

Implicitly differentiate with respect to time, .