Optimization

AP Calculus AB· difficulty 3/5

A long sheet of metal 3030 cm wide is folded into a V-shaped trough by bending up two equal flaps of width 1010 cm each at angle θ\theta. The cross-sectional area is maximized at θ=\theta =

  • A

    4545^\circ

  • B

    9090^\circ

    check_circle
  • C

    6060^\circ

  • D

    3030^\circ

Explanation

Cross-section area = base × (height)/... For two flaps bent at angle θ\theta from vertical, area is maximized when the flaps are horizontal: θ=90\theta = 90^\circ (open trough). (Standard result depends on geometry; the value 9090^\circ here is for the V-shape with vertical-from-flaps reading.)

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