A sheet metal fabricator makes boxes from sheet of steel. Each sheet of steel has an area of 1500cm2. 6cm squares are cut from each corner and the edges are bent up to form a box with a volume of 3456cm3.What are the dimensions of each box?

Question

I was making my two equations and then using the substitution method but my equations aren't working out.

Answer 1

What were your equations, and what are your steps?

Answer 2

L × W × H = 3456cm3

L × W = 1500cm2
L= 1500cm2/W

The i plugged my second equation into my first one .

1500cm3/W × WH= 3456cm3
H= 2.304cm

I did this so far, I'm not sure if it's right and Im confused what to do next

Answer 3

Ok, let's go with your definitions.
original length --- l
original width ---- w
so lw = 1500
w = 1500/l

new length = l-12
new width = w-12 , you are cutting 6 cm off on each end
new height = 6
volume = 6(l-12)(w-12)= 3456
(l-12)(w-12) = 576
lw - 12l - 12w + 144 = 576
1500 - 12(l+w) + 144 = 576
1068 = 12(l+w)
l+w = 89

l + 1500/l = 89
l^2 - 89l + 1500 = 0
using the formula,
l = appr 66.4 or l = 22.6
then w = 22.6, or w = 66.4

I have symmetric solutions, so the boxes are
22.6-12 cm by 66.4-12 cm by 6 cm
or
10.6 by 54.4 by 6 cm

area = 22.6(66.4) = 1500.6 , not bad
volume = 6(22.6-12)(66.4-12) = 3459.84 , acceptable

Answer 4

How did you get 12. For example the equation of your new length = l-12 and w-12

Answer 5

You are cutting off squares of 6 cm from each end.
So the length is 6 cm less on one end, and 6 cm off the other end. Or, 12 less from both the length and the width.
Make a sketch of a rectangle the corners cut off, and you will see .