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Find the falling water level in an inverted cone

A vessel containing water has the shape of an inverted right circular cone with base radius 2 m2\text{ m} and height 5 m5\text{ m}. Water flows from its vertex at 0.2 m3/s0.2\text{ m}^3/\text{s}. Find the exact rate at which the water level is dropping when the water depth is 4 m4\text{ m}.

CJC · Lecture · Example 13

Draw and label the variables, use the constraint to reduce to one variable, then differentiate.

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