You have to wrap gift boxes for your club project. Each box is 4.5 inches wide, 7 inch long, and 4 inches tall. What size sheet of wrapping paper do you need to cut to cover the
box?
Gift wrap paper comes in sheets which are 30 inches wide and 36 inches long. How should you cut your sheet to make the best use of the paper?
You'll have to calculate it taking into account the different ways you could wrap the box.
If you wrap it around the perimeter perpendicular to the 7inch length, and then closing on the two 4.5x4 faces,you need wrapping paper with a length of
4.5*2+4*2 = 9+8 = 17
and width
7 + 4 = 11
or 11x17
If you wrap it around the perimeter perpendicular to the 4.5 inch side, and then closing on the two 7x4 inch sides, you need wrapping paper with a length of
7*2+4*2 = 14+8 = 22
and width of
4.5 + 4 = 9.5
or 22x9.5
If you wrap it around the perimeter perpendicular to the 4 inch side, and then closing on the two 7x4.5 inch sides, you need wrapping paper with a length of
4.5*2 + 7*2 = 14+9 = 25
and width
4+4.5 = 9.5
or 25x9.5
So you have three possibilites to wrap the gift, with sheet sizes
25x9.5
22x9.5
11x17
So 25x9.5 is out, because the other two sheets are smaller.
If you use the 22x9.5 size, you could cut three out of each 30x36 sheet of wrapping paper
If you use 11x17, you could cut out 4 out of each 30*36 sheet of wrapping paper
To determine the size of the wrapping paper needed to cover the box, you need to find the surface area of the box, including the top, bottom, and sides.
The surface area of a rectangular box can be calculated by summing up the areas of all its faces. The formula to find the surface area of a rectangular box is:
Surface Area = 2 * (length * width + length * height + width * height)
Now, let's calculate the surface area for the given box dimensions:
Length = 7 inches
Width = 4.5 inches
Height = 4 inches
Surface Area = 2 * (7 * 4.5 + 7 * 4 + 4.5 * 4)
Surface Area = 2 * (31.5 + 28 + 18)
Surface Area = 2 * 77.5
Surface Area = 155 square inches
To wrap the box completely, you will need a sheet of wrapping paper that has a surface area greater than or equal to 155 square inches.
Now, let's consider the size of the wrapping paper sheets available, which are 30 inches wide and 36 inches long.
To make the best use of the paper, you should cut it in a way that minimizes waste and covers the box effectively.
Since the width of the box is 4.5 inches and the wrapping paper is 30 inches wide, you can cut strips of width 4.5 inches from the paper. Since you need to cover all six faces of the box, you will need six strips of wrapping paper.
Next, considering the length of the box, which is 7 inches, it is shorter than the length of the wrapping paper sheet (36 inches). Therefore, you can cut one lengthwise strip of the wrapping paper from the full length of 36 inches.
To summarize:
- Cut six strips of wrapping paper with a width of 4.5 inches from the sheet.
- Cut one strip of wrapping paper with a length of 36 inches from the sheet.
This way, you will effectively use the wrapping paper while ensuring sufficient coverage for the box.