Canadian Forces Aptitude Test (CFAT) Practice

A box measuring 3 cm wide, 2 cm deep, and 4 cm high has all sides doubled in length. What is the total surface area of the larger box?

1. 104 cm²

2. 208 cm²

3. 48 cm²

4. 96 cm²

The correct answer is: 208 cm²

To determine the total surface area of the larger box after the dimensions have been doubled, we first need to calculate the original dimensions of the box, which are 3 cm wide, 2 cm deep, and 4 cm high. When these dimensions are doubled, the new dimensions become: - Width: \(3 \text{ cm} \times 2 = 6 \text{ cm}\) - Depth: \(2 \text{ cm} \times 2 = 4 \text{ cm}\) - Height: \(4 \text{ cm} \times 2 = 8 \text{ cm}\) The formula for the total surface area of a rectangular box is given by: \[ \text{Surface Area} = 2(w \cdot h + w \cdot d + h \cdot d) \] Substituting the new dimensions into this formula: \[ \text{Surface Area} = 2(6 \cdot 8 + 6 \cdot 4 + 8 \cdot 4) \] Now, calculate each term: - \(6 \cdot 8 = 48\) - \(6 \cdot 4 =