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AP Calculus AB· difficulty 3/5

A snowball's radius melts at −0.5 cm/min-0.5~\text{cm/min}. When r=3 cmr = 3~\text{cm}, the surface area changes at (use S=4πr2S = 4\pi r^2):

  • A

    −24π cm2/min-24\pi~\text{cm}^2/\text{min}

  • B

    −3π cm2/min-3\pi~\text{cm}^2/\text{min}

  • C

    −12π cm2/min-12\pi~\text{cm}^2/\text{min}

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  • D

    −36π cm2/min-36\pi~\text{cm}^2/\text{min}

Explanation

dS/dt=8πr dr/dt=8π(3)(−0.5)=−12πdS/dt = 8\pi r\,dr/dt = 8\pi(3)(-0.5) = -12\pi.

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