Question

Suppose Kari is buying a gift to give the mayor for his new office. She puts the gift into a box that measures 3 feet by 2.5 feet by 1 foot, but the roll of wrapping paper she has is only 30 square feet. Will this be enough to wrap the gift box?

Steps shown correctly (3 points)
Correct answer stated (3 points)
Clear and logical explanation of the process (4 points)

Answer 1

Explanation:

In this case, the box has three pairs of equal-sized faces: the top and bottom, the front and back, and the sides.

The dimensions of the box are as follows:

Length = 3 feet

Width = 2.5 feet

Height = 1 foot

Let's calculate the surface area of the box:

Top and bottom faces: Length x Width = 3 ft x 2.5 ft = 7.5 square feet

Front and back faces: Length x Height = 3 ft x 1 ft = 3 square feet

Side faces: Width x Height = 2.5 ft x 1 ft = 2.5 square feet (each)

Since there are two side faces, their combined area is: 2 x 2.5 square feet = 5 square feet

Total surface area of the box: 2(7.5 square feet) + 2(3 square feet) + 5 square feet = 15 square feet + 6 square feet + 5 square feet = 26 square feet

The available wrapping paper has an area of 30 square feet. Since the surface area of the box is 26 square feet, the roll of wrapping paper is indeed sufficient to wrap the gift box, with some extra paper left over.