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An open box is to be constructed by removing equal squares from each corner of a 5 metre by 7 metre rectangular sheet of aluminium and folding up the sides. Find the volume of the largest such box.

Manvendra Singh chahar , 12 Years ago
Grade Upto college level
anser 2 Answers
SHAIK AASIF AHAMED
let the length of square to be cut is x metres
volume of the box can be represented as
V=(x)(5-2x)(7-2x)......................(1)
V=4x3-24x2+35x
to find maximum volume differentiate V and make it equal to zero
V1=12x2-48x+35=0
we get x=23/24
by substituting x=23/24 in (1) we get
Volume of largest box V=15 m3
Last Activity: 11 Years ago
SHAIK AASIF AHAMED
let the length of square to be cut is x metres

volume of the box can be represented as

V=(x)(5-2x)(7-2x)......................(1)

V=4x3-24x2+35x

to find maximum volume differentiate V and make it equal to zero

V1=12x2-48x+35=0

we get x=23/24

by substituting x=23/24 in (1) we get

Volume of largest box V=15 m3
Thanks and Regards
Shaik Aasif
askIITians Faculty
Last Activity: 11 Years ago
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