Math Problem Statement
Sand is falling from a conveyor onto a sand pile that has the shape of a cone where the radius is always three times the height. If sand is being poured at the rate of 20 cu. ft./min. how fast is the base radius changing at the moment when there is 200 cu. ft of sand in the pile?
Solution
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Math Problem Analysis
Mathematical Concepts
Related Rates
Geometry
Differentiation
Formulas
Volume of a cone: V = (1/3)πr^2h
r = 3h (relationship between radius and height)
dV/dt = 9πh^2(dh/dt)
dr/dt = 3(dh/dt)
Theorems
Chain Rule for differentiation
Volume formula for cones
Suitable Grade Level
Grades 11-12 (Advanced Calculus)
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