Final Answer:
C) 297.5in² because the surface area of the cereal box is 297.5 square inches.
Step-by-step explanation:
To find the surface area of the cereal box, you can use the formula for the surface area of a rectangular prism, which is given as:
Surface Area = 2 * (length * width + length * height + width * height)
Given:
Height = 17.5 inches
Length = 9 inches
Width = 3.5 inches
Plugging the values into the formula:
Surface Area = 2 * (9 * 3.5 + 9 * 17.5 + 3.5 * 17.5)
Surface Area = 2 * (31.5 + 157.5 + 61.25)
Surface Area = 2 * 250.25
Surface Area = 500.5 square inches
However, this formula calculates the total surface area, including the inside and outside of the box. Since we only need the material for one box, we exclude the area of the bottom, as that won't require additional material for the box.
The bottom of the box has an area of length * width, which is 9 * 3.5 = 31.5 square inches.
Subtracting the area of the bottom from the total surface area:
Total Surface Area - Bottom Area = 500.5 - 31.5 = 469 square inches
Therefore, the amount of material needed for one box is 469 square inches. Hence, therefore option c is correct.