physics

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The radius of sphere at therate of 4cm per second .at what ratis its surface area chang when theradius is 6cm

  • physics -

    You seem to have left out some words in your question, such as:

    The radius of sphere IS INCREASING at the rate of 4cm per second.

    Surface area is
    A= 4*pi*R^2

    The rate of increase of surface area is
    dA/dt = 8*pi*R*(dR/dt)

    Plug in 6 cm for R, and dR/dt = 4 cm/s, and compute

  • physics -

    R=4t (cm)
    6=4t
    t=1.5 s.
    A=4πR²=4π(4t)²=
    =64πt²=64π(1.5)²=452.4 cm²

  • physics -

    dA/dt = 64πt²=128 πt=128 π•1.5=603.2 cm²/s

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