A square piece of cardboard with side 12 cm has a small square of 2 cm cut out from each of the corners. The resulting flaps are turned up to make a box 2 cm deep. The volume of the box is:

Options

A. `94 cm^(3)`
B. `102 cm^(3) `
C. `128 cm^(3) `
D. `112 cm^(3)`

Answer

To find the volume of the box formed by cutting out squares from the corners of a cardboard and folding up the flaps, follow these steps:

### Step 1: Determine the dimensions of the cardboard
The original square piece of cardboard has a side length of 12 cm.

### Step 2: Calculate the new dimensions after cutting
Since a square of 2 cm is cut from each corner, the length and width of the base of the box will be reduced by 2 cm from each side.

- New length = Original length - 2 * (size of cut square)
- New length = 12 cm - 2 * 2 cm = 12 cm - 4 cm = 8 cm

So, the new dimensions of the base of the box are 8 cm by 8 cm.

### Step 3: Determine the height of the box
The height of the box is equal to the size of the square cut out from the corners, which is 2 cm.

### Step 4: Calculate the volume of the box
The volume \( V \) of a box is given by the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]

Substituting the values:
\[ V = 8 \text{ cm} \times 8 \text{ cm} \times 2 \text{ cm} \]

Calculating this gives:
\[ V = 64 \text{ cm}^2 \times 2 \text{ cm} = 128 \text{ cm}^3 \]

### Final Answer
The volume of the box is **128 cm³**.

---