To find out how many 1 inch by 1 inch squares Anna can cut from the cereal box that is a rectangular prism, we first need to calculate the volume of the box.
The formula for the volume \( V \) of a rectangular prism is given by:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Given the dimensions:
- Length = 10 in.
- Width = 4 in.
- Height = 12 in.
Now, substituting these values into the formula:
\[ V = 10 , \text{in} \times 4 , \text{in} \times 12 , \text{in} = 480 , \text{in}^3 \]
Since each small square has an area of \( 1 , \text{in}^2 \) and accounts for the thickness, we can use the volume to determine how many 1 in. squares can fit into the box.
Each 1 inch square occupies 1 cubic inch of volume (considering thickness), so the total number of 1 in. squares we can fit is equal to the volume of the box:
\[ \text{Number of squares} = V = 480 \]
None of the provided options in the multiple-choice responses seem correct, as the correct answer is 480 squares.
However, if the question instead referred to only the surface area squares that can be cut from the external faces of the box, we would proceed to calculate the surface area:
The formula for the surface area \( A \) of a rectangular prism is given by:
\[ A = 2 \times (\text{length} \times \text{width} + \text{length} \times \text{height} + \text{width} \times \text{height}) \]
Calculating:
- \( \text{length} \times \text{width} = 10 , \text{in} \times 4 , \text{in} = 40 , \text{in}^2 \)
- \( \text{length} \times \text{height} = 10 , \text{in} \times 12 , \text{in} = 120 , \text{in}^2 \)
- \( \text{width} \times \text{height} = 4 , \text{in} \times 12 , \text{in} = 48 , \text{in}^2 \)
Add these areas:
\[ A = 2 \times (40 + 120 + 48) = 2 \times 208 = 416 , \text{in}^2 \]
Thus, 416 squares can be cut from the surface area of the box.
So, for the provided options, the answer is 416 squares.
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