# math

Identical square are cut from each corner of an 8 inch by 11.75inch rectangular piececof cardboard.the sides are folded up to make a box with no top . if the volume of the resulting box is 63.75 cubic inches how long is the edge of each square that is cut off?

1. 👍
2. 👎
3. 👁
1. let the size of the cut-out be a square of side x inches

base = (8-2x) by (11.75 - 2x) and the height is x

x(8-2x)(11.75-2x) = 63.75
x(94 - 39.5x + 4x^2) = 63.75
94x - 39.5x^2 + 4x^3 - 63.75 = 0

don't know what method you know to solve a cubic, I ran it through Wolfram and got 3 real answers
x = 1.26139
x = 1.875 , and
x = 6.73861 --->that would give you a negative length

subbing in the other x's, will give us 63.75 for both answers.

so you can cut off either 1.26139 inches or 1.875 inches

1. 👍
2. 👎
2. Identical square are cut from each corner of an 8 inch by 11.75inch rectangular piececof cardboard.the sides are folded up to make a box with no top . if the volume of the resulting box is 63.75 cubic inches how long is the edge of each square that is cut off?

1. 👍
2. 👎
3. Thats good.....

1. 👍
2. 👎
4. Zzgxufufgiuff

1. 👍
2. 👎

## Similar Questions

1. ### 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

2. ### math

an open rectangular box is to be formed by cutting identical squares, each of side 2 in, one from each corner of a rectangular piece of cardboard, and then turning up the ends. If the area of the piece of cardboard is 160 in² and

3. ### math

a 5cm by 5cm square is cut from each corner of a rectangular piece of cardboard.the sides are folded up to make an open box with a maximum volume.if the perimeter of the base is 50cm,what are the dimensions of the box.

4. ### calculus

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 14 in. long and 6 in. wide, find the dimensions of the box

1. ### math

An open box is made from a rectangular piece of cardboard measuring 16 cm by 10cm. Four equal squares are to be cut from each corner and flaps folded up. Find the length of the side of the square which makes the volume of the box

2. ### Pre-calculus

A square of size x inches is cut out of each corner of an 8in by 12in piece of cardboard, and the sides are folded up to form an open-topped box. Determine the dimensions of the cut-out squares that will produce the box of maximum

A pizza box top with a square base is to be made from a rectangular sheet of cardboard by cutting six 1-inch squares from the corners and the middle sections and folding up the sides. If the area of the base is to 144 in^2, what

4. ### Math HELP!!

Chuck needs to cut a piece of cardboard for an art project at school. He has four pieces of cardboard that he can cut from: 6 inches, 5 inches, 7 inches, and 3 inches. If the length of the cardboard he needs is √35 inches, which

1. ### college algebra

An open box is made from a square piece of cardboard 20 inches on a side by cutting identical squares from the corners and turning up the sides.(a) Express the volume of the box, V , as a function of the length of the side of the

2. ### Math

a rectangular piece of cardboard is twice as long as it is wide . from each of its for corners, a square piece 3 inches on a side cut out. the flaps at each corner are then turned up to form an open box. if the volume of the box

3. ### Precalculus

From a rectangular piece of cardboard having dimensions a × b, where a = 40 inches and b = 70 inches, an open box is to be made by cutting out an identical square of area x2 from each corner and turning up the sides (see the

4. ### Math

A pizza box with a square base is to be made from a rectangular sheet of cardboard by cutting six 1-inch squares from the corners and the middle sections and folding up the sides (see the figure). If the area of the base is to be