Calculus

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At a certain instant, each edge of a cube is 5 inches long and the volume is increasing at the rate of 2 cubic inches per minute. How fast is the surface area of the cube increasing?

  • Calculus -

    a = 6s^2
    da/dt = 12s ds/dt
    da/dt = 12*5*2 = 120 in^2/min

  • Calculus -

    V = s^3
    dV/dt = 3v^2 ds/dt
    when s = 5, dV/dt = 2
    2 = 3(25) ds/dt
    ds/dt = 2/75

    A = 6s^2
    dA/dt = 12s ds/st
    = 12(5) (2/75) = 8/5 inches^2 / min

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