The radius of a right circular cone is increasing at a rate of 2 inches per second and its height is decreasing at a rate of 2 inches per second. at what rate is the volume of the cone changing when the radius is 30 inches and the height is 40 inches?

Question

Mathematics

Ayala

21 March, 13:12

The radius of a right circular cone is increasing at a rate of 2 inches per second and its height is decreasing at a rate of 2 inches per second. at what rate is the volume of the cone changing when the radius is 30 inches and the height is 40 inches?

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Answers (1)

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Marin Snyder · Answer 1

V = (1/3) πr²h

∴ dV/dt

= (π/3) [r² (dh/dt) + h2r (dr/dt) ]

= (π/3) [ (30) ² (-2) + 40 (2) (30) (2) ]

= (π/3) [-1800+4800]

=1600π in³/sec

Answer: 1600π in³/sec