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March 29, 2017

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Air is being pumped into a spherical balloon so that its volume increases at a rate of 80 cubic centimeters per second. How fast is the surface area of the balloon increasing when its radius is 8 cm?

  • calculus - ,

    A = surface area = (4/3) pi r^2
    so
    d A/dt = (8/3) pi r dr/dt

    now get dr/dt from:

    D Volume = surface area*dr=(4/3) pi r^2 dr
    so
    dV/dt = (4/3)pi r^2 dr/dt

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