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7-79.

conical sand pile 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? Homework Help ✎

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, .