Math Problem Statement
The height of a cone is increasing at a constant rate of 4 in./s and the volume is increasing at a rate of 239 in.³ per second at the instant when the radius of the cone is 10 inches and the volume is 527 in.³ what is the rate of change of the radius?
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Related Rates
Differentiation
Geometry
Calculus
Formulas
Volume of a cone: V = (1/3)πr²h
Differentiation: dV/dt = (1/3)π(2r * h * dr/dt + r² * dh/dt)
Theorems
Chain Rule
Implicit Differentiation
Suitable Grade Level
Grades 11-12 (Precalculus, Calculus)
Related Recommendation
Related Rates: Cone Volume with Changing Radius and Height
Find the Rate of Change of Volume of a Cone with Varying Radius and Height
Calculating Rate of Change of Cone's Volume with Changing Radius and Height
Solving Related Rates Problem: Volume of Water in an Inverted Cone
Related Rates: Finding Rate of Change of Cone Radius