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)

Answer 1

To find the number of complete boxes that can be wrapped with one roll of wrapping paper, we first need to calculate the area of the wrapping paper. The area of the wrapping paper can be calculated by multiplying the length and width of the paper.

Area of wrapping paper = length × width = 25 in. × 405 in. = 10,125 in²

Next, we need to calculate the surface area of one box. The surface area of a rectangular prism can be calculated using the formula: surface area = 2(length × width) + 2(length × height) + 2(width × height)

Surface area of one box = 2(16 in. × 14 in.) + 2(16 in. × 6 in.) + 2(14 in. × 6 in.)
= 2(224 in²) + 2(96 in²) + 2(84 in²)
= 448 in² + 192 in² + 168 in²
= 808 in²

Finally, divide the area of the wrapping paper by the surface area of one box to find the number of complete boxes that can be wrapped.

Number of complete boxes = Area of wrapping paper / Surface area of one box
= 10,125 in² / 808 in²
= 12.53

Since we cannot have a fraction of a box, only 12 complete boxes can be wrapped with one roll of wrapping paper.