Asked by ERICK

Find the largest volume of the open box to be made from cutting equal squares from 3m by 8m sheet then folding it up.

Answers

Answered by mathhelper
size of cut-out squares:
x by x m
V = x(3-2x)(8-3x), 0 < x < 3/2
= x(24 - 25x + 6x^2)
= 24x - 25x^2 + 6x^3

dV/dx = 24 - 50x + 18x^2
= 0 for a max of V
9x^2 - 25x + 12 = 0

by formula I got x = .617 and 2.16 , reject the 2.16 since it will
produce a negative dimension

Sub that into V = ...
to find that max volume

check my arithmetic
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