# Math

An open-topped box can be created by cutting congruent squares from each of the four corners of a piece of cardboard that has dimensions of 20cm by 30cm and folding up the sides. Determine the dimensions of the squares that must be cut to create a box with a volume of 1008cm^3.
length=30-2x
width=20-2x
h=x
I don't get this because x and cm aren't interchangeable digits.

1. 👍
2. 👎
3. 👁
1. no idea what your complaint is about. x is a variable, and its units are cm. Multiply the three expressions and you get cm^3.

x(20-2x)(30-2x) = 1008
4x^3 - 100x^2 + 600x - 1008 = 0
scale down by 4:
x^3 - 25x^2 + 150x - 252 = 0

252 = 2*2*3*3*7
The only integer root is x=3, so the required box is

3×14×24 = 1008

1. 👍
2. 👎
2. Actual length = 23•8m 1cm to 2m

1. 👍
2. 👎
3. Why is it always (whatever number -2x)? why the -2x?

1. 👍
2. 👎

## Similar Questions

1. ### calculus

An open box of maximum volume is to be made from a square piece of cardboard, 24 inches on each side, by cutting equal squares from the corners and turning up the sides to make the box. (a) Express the volume V of the box as a

2. ### Calculus

An open box is formed from a piece of cardboard 12 inches square by cutting equal squares out of the corners and turning up the sides, find the dimensions of the largest box that can be made in this way.

3. ### Calculus

A box with an open top is to be made from a square piece of cardboard by cutting equal squares from the corners and turning up the sides. If the piece of cardboard measures 12 cm on the side, find the size of the squares that must

4. ### calculus

An open box is to be made out of a 10-inch by 14-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume.

1. ### Calculus

an open box is made by cutting out squares from the corners of a rectangular piece of cardboard and then turning up the sides. If the piece of cardboard is 12 cm by 24 cm, what are the dimensions of the box that has the largest

2. ### calculus

an open box is to be made from a piece of metal 16 by 30 inches by cutting out squares of equal size from the corners and bending up the sides. what size should be cut out to create a box with the greatest volume? what is the

3. ### calculus

7. A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 40 cm by 60 cm by cutting equal squares from the four corners and turning up the sides. Find the length of the side of

4. ### Calc

An open box is to be made out of a 10-inch by 16-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume.

1. ### mathematics

A square sheet of cardboard with each side a centimeters is to be used to make an open-top box by cutting a small square of cardboard from each of the corners and bending up the sides. What is the side length of the small squares

2. ### Math

You want to create a box without a top from an 8.5 in by 11 in sheet of paper. You will make the box by cutting squares of equal size from the four corners of the sheet of paper. If you make the box with the maximum possible

3. ### math

a rectangular sheet of cardboard 4m by 2m is used to make an open box by cutting squares of equal size from the four corners and folding up the sides.what size squares should be cut to obtain the largest possible volume?

4. ### Calculus

An open box is made by cutting squares of side w inches from the four corners of a sheet of cardboard that is 24" x 32" and then folding up the sides. What should w be to maximize volume of the box? I started by trying to get a