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