calculus

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The volume of a melting cube is decreasing at a rate of 10cm^3/min. How fast is the surface area of the ice cube decreasing when the length of an edge is 30 cm?

  • calculus -

    V = x^3
    dV/dt = 3x^2 dx/dt
    10 = 3x^2 dx/dt
    dx/dt = 10/(3x^2)

    SA = 6x^2
    d(SA)/dt = 12x dx/dt
    dx/dt = d(SA)/dt / (12x)

    d(SA)d/t / (12x) = 10/(3x^2)
    d(SA)/dt = 120x/(3x^2)
    which when x = 30
    = 120(30)/2700 = 4/3 cm/min

  • calculus -

    Thank you so much that was so helpful.

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