a roll of wrapping paper measures 25 in. by 405 in. the boxes being wrapped are 16 in. x 14 in. x 6 in. how many complete boxes can be wrapped with ONE ROLL of wrapping paper?
To wrap a box, we need to cover all six sides of the box with wrapping paper.
The dimensions of the wrapping paper roll are 25 inches by 405 inches.
Let's calculate the amount of wrapping paper needed to wrap one box:
- For the first side, we need a 16-inch by 14-inch piece of wrapping paper.
- For the second side, we need another 16-inch by 14-inch piece of wrapping paper.
- For the third side, we need a 16-inch by 6-inch piece of wrapping paper.
- For the fourth side, we need another 16-inch by 6-inch piece of wrapping paper.
- For the fifth side, we need a 14-inch by 6-inch piece of wrapping paper.
- For the sixth side, we need another 14-inch by 6-inch piece of wrapping paper.
To calculate the total wrapping paper needed, we add the areas of these six pieces:
Area of the first side = 16 inches * 14 inches = 224 square inches
Area of the second side = 16 inches * 14 inches = 224 square inches
Area of the third side = 16 inches * 6 inches = 96 square inches
Area of the fourth side = 16 inches * 6 inches = 96 square inches
Area of the fifth side = 14 inches * 6 inches = 84 square inches
Area of the sixth side = 14 inches * 6 inches = 84 square inches
Total wrapping paper needed to wrap one box = 224 + 224 + 96 + 96 + 84 + 84 = 808 square inches.
Now, we can divide the total area of the wrapping paper roll (25 inches * 405 inches = 10125 square inches) by the area needed to wrap one box (808 square inches) to find out how many boxes can be wrapped with one roll of wrapping paper:
10125 square inches / 808 square inches ≈ 12.52.
So, approximately 12 complete boxes can be wrapped with one roll of wrapping paper.