To find out how many 1-inch squares can be cut from the cereal box, we need to calculate the volume of the box and then find out how many 1-inch cubes fit into that volume.
The dimensions of the box are:
- Length = 10 inches
- Width = 4 inches
- Height = 12 inches
The volume \( V \) of the rectangular prism can be calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Plugging in the values:
\[ V = 10 \times 4 \times 12 \] \[ V = 480 \text{ cubic inches} \]
Since each square has a side length of 1 inch, each 1-inch square occupies 1 cubic inch. Therefore, the number of 1-inch squares that can be cut from the box is equal to the volume of the box:
\[ \text{Number of squares} = 480 \]
It appears that "480 squares" is not one of the options provided in the responses. The options listed (400, 417, 416, 401) do not match the calculated value of 480 squares.
If the only concern is counting the number of 1-inch squares on the surface area of the box instead, that would be different. The surface area of the rectangular prism will be:
\[ \text{Surface Area} = 2(lw + lh + wh) \] \[ = 2(10 \times 4 + 10 \times 12 + 4 \times 12) \] Calculating this, \[ = 2(40 + 120 + 48) = 2(208) = 416 \text{ square inches} \]
If we are talking about the surface area, then Anna can indeed cut out 416 squares from the surface area of the box.
Thus, the answer is 416 squares if we are referring to the surface area.