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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.

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.

Grade:Upto college level

2 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
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
SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
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

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