A packaging company is manufacturing cardboard boxes with no 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 square inches of waste will there be from each sheet of cardboard after all the rectangular nets that contain the crosses have been cut away?(Enter the whole number only with no units in the box.)
Question
A packaging company is manufacturing cardboard boxes with no 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 square inches of waste will there be from each sheet of cardboard after all the rectangular nets that contain the crosses have been cut away?(Enter the whole number only with no units in the box.)
Solution
To solve this problem, we first need to understand the size of the box and the size of the cardboard sheet.
The box is 3" long, 2" wide and 1" high. When we unfold this box into a flat net, it will look like a cross with a 2" by 3" rectangle in the center (the base of the box), and four 1" by 2" rectangles (the sides of the box) attached to each side of the base. So, the total area of the net is (23) + 4(1*2) = 6 + 8 = 14 square inches.
The sheet of cardboard is 1 yard by 1 yard. Since 1 yard is equal to 36 inches, the total area of the sheet is 36" * 36" = 1296 square inches.
Now, we need to find out how many box nets can be cut from the sheet. To do this, we divide the total area of the sheet by the area of one net: 1296 / 14 = 92.57. Since we can't cut a fraction of a net, we round this down to 92 nets.
The total area of these 92 nets is 92 * 14 = 1288 square inches. So, the waste from each sheet of cardboard is the total area of the sheet minus the total area of the nets: 1296 - 1288 = 8 square inches.
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