Question

which expression represents the total surface area of the cube shown? (9·9)+(9·9) 9(9·9) 6(9·9) 2(9·9)+2(9·9)

Explanation:

Step1: Recall cube surface area formula

A cube has 6 identical square faces. The area of one square face with side length \( s \) is \( s \times s \) (or \( s^2 \)). For a cube with side length 9 m, the area of one face is \( 9 \times 9 \).

Step2: Calculate total surface area

Since there are 6 faces, the total surface area (TSA) is the area of one face multiplied by 6. So \( \text{TSA} = 6 \times (9 \times 9) \), which is \( 6(9 \cdot 9) \).

Step3: Analyze other options

• \( (9 \cdot 9)+(9 \cdot 9) \): Only 2 faces, not total.
• \( 9(9 \cdot 9) \): 9 faces, incorrect.
• \( 2(9 \cdot 9)+2(9 \cdot 9) \): Equals \( 4(9 \cdot 9) \), 4 faces, incorrect.

Answer:

\( 6(9 \cdot 9) \) (the third option)