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Math (Calculus)

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A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.3 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 10 cm.

Can someone help & explain how to solve this question? Please.

  • Math (Calculus) - ,

    v = 4/3 pi r^3
    dv/dt = 4pi r^2 dr/dt
    = 4pi * 25cm^2 * -0.3cm/min
    = -30pi cm^3/min

  • Math (Calculus) - ,

    small correction to Steve's solution

    d(diameter)/dt = -.3
    dr/dt = -.15

    so dv/dt = 4π(25)(-.15) = -15π cm^3/min

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