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20 September, 17:45

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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  1. 20 September, 18:27
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    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
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