Math Problem Statement
it is given that a container is in the from of an inverted right circular cone iwht base radius 4cm and height 16cm. the contianer is held vertically. initially, the container is full filled with water. then the water is pumped out from the container at a constant rate of 60cm^3 /s. let v cm^3 and h cm be the volume and the depth of water in the container respectively after t seconds. find the depth of water when the rate of increase of the depth of water is 12 cm/s
Solution
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Math Problem Analysis
Mathematical Concepts
Geometry
Related Rates
Volume of Cones
Differentiation
Formulas
Volume of cone: V = (1/3)πr^2h
Ratio of radius to height: r/h = 1/4
Differentiation: dV/dt = π/16 * h^2 * dh/dt
Theorems
Related Rates Theorem
Volume of a Cone
Suitable Grade Level
Grades 10-12
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