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If 1,200 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
If 1,200 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
Thevolumeof theopen-top boxis the amount of space in it.Thelargest possible volumeof theboxis 4000 cubic centimetersThesurface areaof anopen-top boxis:So, we have:The box has asquare base.So, we have:TheexpressionbecomesMake the subjectThevolumeof theboxis:So, we have:SubstituteExpandSplitDifferentiateSet to 0Rewrite as:Multiply through by 4Divide both sides by 3Take square roots of both sidesRecall that:So, we have:Recall that:So, we have:Hence, thelargest possible volumeof theboxis 4000 cubic centimetersRead more aboutvolumesat:brainly.com/question/2198651...
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