To find out how many 1 in. squares Anna can cut from the cereal box, we first need to calculate the total surface area of the rectangular prism.
The formula for the surface area \( S \) of a rectangular prism is given by:
\[ S = 2lw + 2lh + 2wh \]
Where:
- \( l \) is the length of the prism,
- \( w \) is the width of the prism,
- \( h \) is the height of the prism.
For the cereal box:
- \( l = 10 \) in,
- \( w = 4 \) in,
- \( h = 12 \) in.
Substituting these values into the formula:
\[ S = 2(10)(4) + 2(10)(12) + 2(4)(12) \]
Calculating each term:
- \( 2(10)(4) = 80 \)
- \( 2(10)(12) = 240 \)
- \( 2(4)(12) = 96 \)
Now, we sum these values to find the total surface area:
\[ S = 80 + 240 + 96 = 416 \text{ square inches} \]
Since each small square has an area of \( 1 \text{ in}^2 \), the number of 1 in. squares that can be cut from the surface area of the cereal box is equal to the total surface area:
\[ \text{Number of squares} = 416 \]
Therefore, the total number of 1 in. squares Anna can cut from the cereal box is
\[ \boxed{416} \]