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An inverted conical water tank with a height of 6 ft and a radius of 3 ft is drained through a hole in the vertex at a rate of 6 ft /s (see figure). What is the rate of change of the water depth when the water depth is 3 ft? (Hint: Use similar triangles.) 3 ft 6 ft Outflow 6 ft /s

An inverted conical water tank with a height of 6 ft and a radius of 3 ft is drained through a hole in the vertex at a rate of 6 ft /s (see figure). What is the rate of change of the water depth when the water depth is 3 ft? (Hint: Use similar triangles.) 3 ft 6 ft Outflow 6 ft /s

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterP: Prologue: Calculator Arithmetic
Section: Chapter Questions
Problem 18E: When the Radius Increases a. A rope is wrapped tightly around a wheel with radius of 2 feet. If the...
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An inverted conical water tank with a height of 6 ft and a radius of 3 ft is drained Let V be the volume of water in the tank and let h be the depth of the water. Write an equation that relates V and h. ,3 through a hole in the vertex at a rate of 6 ft° /s (see figure). What is the rate of change of the water depth when the water depth is 3 ft? (Hint. Use similar triangles.) 3. V = 12 3 ft (Type an exact answer, usingn as needed.) Differentiate both sides of the equation with respect to t. dV dh 6 ft dt 4 dt When the water depth is 3 ft, the rate of change of the water depth is about ft/s. (Round to the nearest hundredth as needed.) Outflow 6 ft/s
Transcribed Image Text:An inverted conical water tank with a height of 6 ft and a radius of 3 ft is drained Let V be the volume of water in the tank and let h be the depth of the water. Write an equation that relates V and h. ,3 through a hole in the vertex at a rate of 6 ft° /s (see figure). What is the rate of change of the water depth when the water depth is 3 ft? (Hint. Use similar triangles.) 3. V = 12 3 ft (Type an exact answer, usingn as needed.) Differentiate both sides of the equation with respect to t. dV dh 6 ft dt 4 dt When the water depth is 3 ft, the rate of change of the water depth is about ft/s. (Round to the nearest hundredth as needed.) Outflow 6 ft/s
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