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AP Calculus AB· difficulty 3/5

A circle's radius grows at 2 cm/s2~\text{cm/s}. When r=5 cmr = 5~\text{cm}, the area's rate of change is

  • A

    20π cm2/s20\pi~\text{cm}^2/\text{s}

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  • B

    10π cm2/s10\pi~\text{cm}^2/\text{s}

  • C

    25π cm2/s25\pi~\text{cm}^2/\text{s}

  • D

    50π cm2/s50\pi~\text{cm}^2/\text{s}

Explanation

A=πr2A = \pi r^2, dA/dt=2πr⋅dr/dt=2π(5)(2)=20π cm2/sdA/dt = 2\pi r \cdot dr/dt = 2\pi(5)(2) = 20\pi~\text{cm}^2/\text{s}.

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