calculus

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a spherical balloon filled with gas has a leak that permits the gas to escape at a rate of 1.5 cubic meters per minute. how fast is the surface area of the balloon shrinking when the radius is 4 meters?

  • calculus -

    v = 4/3 pi r^3
    dv/dt = 4pi r^2 dr/dt
    -1.5 = 4pi (16) dr/dt
    dr/dt = -1.5/64pi

    a = 4pi r^2
    da/dt = 8pi r dr/dt
    = 8pi (4) (-1.5/64pi)
    = -3/4 m^2/min

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