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AP Calculus AB· difficulty 3/5

A cylinder's radius grows at 1 cm/s1~\text{cm/s} and its height stays at 10 cm10~\text{cm}. When radius is 4 cm4~\text{cm}, volume changes at

  • A

    160π cm3/s160\pi~\text{cm}^3/\text{s}

  • B

    8π cm3/s8\pi~\text{cm}^3/\text{s}

  • C

    40π cm3/s40\pi~\text{cm}^3/\text{s}

  • D

    80π cm3/s80\pi~\text{cm}^3/\text{s}

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Explanation

V=πr2hV = \pi r^2 h, hh constant. dV/dt=2πrh dr/dt=2π(4)(10)(1)=80πdV/dt = 2\pi r h\,dr/dt = 2\pi(4)(10)(1) = 80\pi.

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