A roll of wrapping paper measures 25 in. × 405 in. The boxes being wrapped are 16 in. × 14 in. × 6 in. How many complete boxes can be wrapped with one roll of wrapping paper?(1 point)
Calculate the surface area of a cube with 12-inch edges. How many square inches is the surface area?(1 point)
The surface area of a cube can be calculated by finding the area of each face and adding them together. Since all faces of a cube are identical and have equal side lengths, we can find the surface area by multiplying the area of one face by 6 (since a cube has 6 faces).
The area of one face is found by multiplying the side length by itself:
Area of one face = 12 in × 12 in = 144 in²
Therefore, the total surface area of the cube is:
Surface area = Area of one face × 6 = 144 in² × 6 = 864 in².
Thus, the surface area of a cube with 12-inch edges is 864 square inches. Answer: \boxed{864}.
To determine how many complete boxes can be wrapped with one roll of wrapping paper, we need to calculate the area of the wrapping paper and the area of the boxes.
The area of the wrapping paper is the product of its length and width:
Area of wrapping paper = 25 in. × 405 in. = 10,125 in²
The boxes have three dimensions: length, width, and height. To find the surface area of the box, we need to calculate the area of each face and then add them together.
The area of one face of the box is the product of its length and width:
Area of one face = 16 in. × 14 in. = 224 in²
Since there are two identical faces on all four sides of the box, we can calculate the surface area of one side by multiplying the area of one face by 2:
Area of one side = 224 in² × 2 = 448 in²
There are four sides to a box, so the total surface area of the box is:
Total surface area of box = 448 in² × 4 = 1792 in²
Now we can determine how many complete boxes can be wrapped with one roll of wrapping paper by dividing the area of the wrapping paper by the total surface area of the box:
Number of complete boxes = Area of wrapping paper / Total surface area of box
= 10,125 in² / 1792 in²
≈ 5.65
Since you cannot wrap a fraction of a box, the number of complete boxes that can be wrapped with one roll of wrapping paper is 5. Answer: \boxed{5}.