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March 27, 2017

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Gas is escaping a round balloon at2units^2/min.How fast is the surface area shrinking when the radius is 12units?

  • Calculus - ,

    Volume = V = (4/3) pi r^3

    area =A = 4 pi r^2
    r = (A/4pi)^.5
    so
    V = (4/3) pi (A/4pi)^1.5

    dV/dt = (4/3)(1/5)(A/4pi)^.5 (dA/dt/4pi)

    here dV/dt = -2
    r = 12 so A = 4 pi(144)
    solve for dA/dt

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