Math Problem Statement
The height of a cylinder is increasing at a constant rate of 7 inches per minute. The volume remains a constant 889 cubic inches. At the instant when the radius of the cylinder is 99 inches, what is the rate of change of the radius? The volume of a cylinder can be found with the equation V, equals, pi, r, squared, h, .V=πr 2 h. Round your answer to three decimal places.
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Related Rates
Differentiation
Formulas
Volume of a cylinder: V = πr^2h
Differentiation of volume with respect to time: dV/dt = π(2rh dr/dt + r^2 dh/dt)
Theorems
Related Rates
Suitable Grade Level
Grade 11-12 or Early College
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