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Optimization

AP Calculus AB· difficulty 3/5

Of all cylinders inscribed in a sphere of radius RR, the maximum volume is at radius r=r =

  • A

    R/2R/\sqrt 2

  • B

    R/3R/\sqrt 3

  • C

    R2/3R\sqrt{2/3}

    check_circle
  • D

    RR

Explanation

With r2+(h/2)2=R2r^2 + (h/2)^2 = R^2, V=πr2hV = \pi r^2 h. Optimization gives r2=2R2/3r^2 = 2R^2/3.

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