Answer:
4in. square x 4in. square x 1in. square
Step-by-step explanation:
By cutting out identical squares (considering 'x') from each corner and bending up the resulting flaps
The dimensions we have will be (see attachment for the figure)
V= (6-2x) (6-2x) x
As, Volume'V' = length (l) x width(w) x height(h)
V= (6x- 2x²)(6-2x)
V= 36x - 12x²-12x²+ 4x³
V=4x³ - 24x²+ 36x
Next is to find dV/dx,therefore we find the derivative and and set it to zero for the maximum volume
dV/dx = 12x² - 48x + 36
setting it to zero
12x² - 48x + 36 =0
x² - 4x + 3=0
x² -3x -x + 3=0
x(x-3) -1(x-3)=0
Either : x-3=0=> x=3
OR : x-1 =0 => x=1
Now, notice that 'x' cannot be 3 , because if we cut 3 inch squares out of the original square, there will be nothing left!
Also, the volume will be 0 then. That is the minimum volume, 0, when we cut all the tin away.
So, x=1
Therefore,
height 'x' = 1in. square
length and width = (6-2x) => 4in. square
