SOLUTION: an open topped box is made from a rectangular piece of cardboard, with the dimensions 24 cm by 30 cm, by cutting congruent squares from each corner and folding up the sides. determ

Question 160326: an open topped box is made from a rectangular piece of cardboard, with the dimensions 24 cm by 30 cm, by cutting congruent squares from each corner and folding up the sides. determine the dimensions of the squares to be cut to create a box with a volume of 1040cm^3
Found 2 solutions by checkley77, ankor@dixie-net.com:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
height=x, base=24*30-4x^2=720-4x^2
x(720-4x^2)=1040
4x^3-720x+1040=0
using approximations we get x=1.47045 cm.
proof:
1.47045(720-4*1.47045^3)=1040
1.47045(720-4*3.17844)=1040
1.47045(720-12.71776)=1040
1.47045*707.28224=1040
1040~1040
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
An open topped box is made from a rectangular piece of cardboard, with the dimensions 24 cm by 30 cm, by cutting congruent squares from each corner and folding up the sides. determine the dimensions of the squares to be cut to create a box with a volume of 1040cm^3
:
Let the side of the removed squares = x
:
The dimension of the box will be: (24-2x) by (30-2x) by x (height)
:
A volume equation, L * W * H
(24-2x) * (30-2x) * x = 1040
FOIL
(720 - 48x - 60x + 4x^2) * x = 1040
:
Multiply by x;
720x - 108x^2 + 4x^3 = 1040
;
4x^3 - 108x^2 + 720x - 1040 = 0
:
Simplify; divide by 4:
x^3 - 27x + 180x - 260 = 0
:
Graphing this would be one way to solve this
:

;
x = 2 cm would work
:
L: 30-4 = 26 cm
W: 24-4 = 20 cm
H: 2 cm
:
Check the volume
(26*20*2 = 1040
:
You can see there is another solution on the graph: x ~ 7.4
The dimensions for that would be
L: 30-14.8 = 15.2
W: 24-14.8 = 9.2
H: 7.4 cm
:
Check vol with this: 15.2*9.2*7.4 = 1035.8 (because not an integer)

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