Questions: A box measures 3 cm × 4 cm × 2 cm. What is the surface area of the box? A) 24 cm^2 B) 52 cm^2 C) 26 cm^2

Transcript text: 16) A box measures $3 \mathrm{~cm} \times 4 \mathrm{~cm} \times 2 \mathrm{~cm}$. What is the surface area of the box? A) $24 \mathrm{~cm}^{2}$ B) $52 \mathrm{~cm}^{2}$ C) $26 \mathrm{~cm}^{2}$

Solution

Solution Steps

Step 1: Identify the dimensions of the box

The box has dimensions $3 \mathrm{~cm} \times 4 \mathrm{~cm} \times 2 \mathrm{~cm}$.

Step 2: Calculate the area of each pair of opposite faces

The area of the first pair of faces (dimensions $3 \mathrm{~cm} \times 4 \mathrm{~cm}$) is: \[ 2 \times (3 \times 4) = 2 \times 12 = 24 \mathrm{~cm}^{2} \]
The area of the second pair of faces (dimensions $3 \mathrm{~cm} \times 2 \mathrm{~cm}$) is: \[ 2 \times (3 \times 2) = 2 \times 6 = 12 \mathrm{~cm}^{2} \]
The area of the third pair of faces (dimensions $4 \mathrm{~cm} \times 2 \mathrm{~cm}$) is: \[ 2 \times (4 \times 2) = 2 \times 8 = 16 \mathrm{~cm}^{2} \]

Step 3: Sum the areas of all faces to find the total surface area

\[ 24 \mathrm{~cm}^{2} + 12 \mathrm{~cm}^{2} + 16 \mathrm{~cm}^{2} = 52 \mathrm{~cm}^{2} \]