A packaging company is manufacturing cardboard boxes without a lid that measure 3" long, 2" wide and 1" high.They will be cut by using a geometric net where each side of the base is simply folded down flat (Like a cross).The boxes will be cut from sheets of cardboard that measure 1 yard by 1 yard.How many boxes can be cut from each sheet?

To solve this problem, we first need to understand the size of the cardboard sheet and the size of each box.

1. Convert the dimensions of the cardboard sheet from yards to inches, since the dimensions of the box are given in inches. There are 36 inches in a yard, so the sheet is 36" x 36".

2. Next, we need to determine the size of the flat box (the geometric net). The box is 3" long, 2" wide, and 1" high. When flattened, it will have a length of 3" (the base) + 1" (one side) + 1" (the other side) = 5". The width will remain 2".

3. Now, we can determine how many boxes can be cut from the sheet. Divide the length of the sheet by the length of the box to get the number of boxes that can be cut lengthwise (36" / 5" = 7.2). Since we can't have a fraction of a box, we round down to 7.

4. Do the same for the width of the sheet and the width of the box (36" / 2" = 18 boxes).

5. Multiply the number of boxes that can be cut lengthwise by the number that can be cut widthwise to get the total number of boxes that can be cut from the sheet (7 x 18 = 126).

So, 126 boxes can be cut from each sheet of cardboard.

To solve this problem, we first need to understand the size of the cardboard sheet and the size of each box.

1. Convert the dimensions of the cardboard sheet from yards to inches, since the dimensions of the box are given in inches. 1 yard is equal to 36 inches. So, the sheet is 36" x 36".

2. Next, we need to determine the size of the flat cardboard piece needed to make each box. The box is 3" long, 2" wide, and 1" high. When the box is unfolded into a flat piece, it forms a cross shape with five squares - one for the base, and four for the sides. Each square is 3" x 2". So, the total area of cardboard needed for each box is 5 * (3" x 2") = 30 square inches.

3. Now, we can calculate how many boxes can be cut from the sheet. The total area of the sheet is 36" x 36" = 1296 square inches. Divide this by the area of each box to find the number of boxes: 1296 / 30 = 43.2.

Since we can't have a fraction of a box, we round down to the nearest whole number. So, 43 boxes can be cut from each sheet of cardboard.