A roll of wrapping paper measures 25in. X 405in. The boxes being wrapped are 16in. X 14in. X 6 in. How many complete boxes can be wrapped with one roll of wrapping paper.
To determine the number of complete boxes that can be wrapped with one roll of wrapping paper, we need to find the area of the wrapping paper and the area of each box.
The area of the wrapping paper is given by the formula length x width, so the area of the wrapping paper is 25in. x 405in. = 10125in².
The boxes have three dimensions: length, width, and height. To wrap one box, you need to cover the surface area of each side of the box. The total surface area of a box is given by the formula 2(length x width + length x height + width x height).
For this particular box, the total surface area is 2(16in. x 14in. + 16in. x 6in. + 14in. x 6in.) = 2(224in² + 96in² + 84in²) = 2(404in²) = 808in².
To find the number of complete boxes that can be wrapped, we divide the area of the wrapping paper by the area of each box: 10125in² / 808in² ≈ 12.52.
Since we can't have fractional boxes, we round down to the nearest whole number. Therefore, one roll of wrapping paper can wrap 12 complete boxes.