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An open box is to be constructed by removing equal squares from each corner of a 3 metre by 8 metre rectangular sheet of aluminium and folding up the sides. Find the volume of the largest such box

An open box is to be constructed by removing equal squares from each corner of a 3 metre by 8 metre rectangular sheet of aluminium and folding up the sides. Find the volume of the largest such box

Grade:Upto college level

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
let the length of square to be cut is x metres
volume of the box can be represented as
V=(x)(3-2x)(8-2x)......................(1)
V=4x3-22x2+24x
to find maximum volume differentiate V and make it equal to zero
V1=12x2-44x+24=0
we get x=2/3
by substituting x=2/3 in (1) we get
Volume of largest box V=200/27 m3
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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