Canadian Forces Aptitude Test (CFAT) Practice

What is the total surface area of a box with doubled dimensions if the original dimensions are 3 cm wide, 2 cm deep, and 4 cm high?

1. 96 cm²

2. 208 cm²

3. 144 cm²

4. 72 cm²

The correct answer is: 208 cm²

To determine the total surface area of a box with doubled dimensions, we first need to calculate the surface area of the original box, which has dimensions of 3 cm wide, 2 cm deep, and 4 cm high. The formula for the surface area \(S\) of a rectangular box is: \[ S = 2(lw + lh + wh) \] where \(l\) is the length, \(w\) is the width, and \(h\) is the height. Using the original dimensions: - Length = 4 cm (height) - Width = 3 cm - Height = 2 cm (depth) Calculating the surface area of the original box gives us: - \( lw = 4 \times 3 = 12 \) - \( lh = 4 \times 2 = 8 \) - \( wh = 3 \times 2 = 6 \) Now substituting back into the formula: \[ S = 2(12 + 8 + 6) = 2(26) = 52 \, \text{cm}² \] Next, we double the dimensions: - New width = 3 cm × 2 =