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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

Manvendra Singh chahar , 10 Years ago
Grade Upto college level
anser 1 Answers
SHAIK AASIF AHAMED

Last Activity: 10 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
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