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A right circular cone has a constant volume. The height h and the base radius r can both vary. Find the rate at which h is changing with respect to r at the instant when r and h are equal.

  • Calculus -

    v = pi/3 r^2 h

    since v is a constant, dv = 0

    0 = 2rh dr + r^2 dh

    When r=h,

    2r^2 dr + r^2 dh = 0
    2dr + dh = 0

    dh = -2dr

    dh/dr = -2

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