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March 25, 2017

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A block of ice is exposed to heat in such a way that the block maintains a similar shape as it metls. The block of ice is initially 2' wide, 2 'high, and 3' long. If the change in the width of the ice is -1/3 ft/hr, find: the amount of time it will tak efor the block of the ice to completely melt.

I found that the rate of change in the volume of the ice block is -3/2 ft^3/hr. Do you just divide the volume of the cube (12 ft^3) by the rate of change of the volume (-3/2 ft^3/hr)?

  • Calculus - ,

    v = w*w*3w/2 = 3/2 w^3
    dv/dt = 9/2 w^2 dw/dt
    = 9/2 * -1/3 = -3/2

    your dv/dt is correct.

    as for your question, consider the units:

    time = ft^3 / ft^3/hr = 12/(3/2) = 8 hr

  • Calculus - ,

    Thank you! That was helpful :)

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