The edges of a cube are 8 meters long. What is the surface area of the cube?

Rationale

The surface area of the cube is 384 m squared.

The surface area of a cube is calculated using the formula \(6a^2\), where \(a\) is the length of one edge. Given that each edge of the cube is 8 meters, the calculation yields a surface area of \(6 \times (8^2) = 6 \times 64 = 384\) square meters.

A (384 m squared) CORRECT

This choice is correct. The surface area of the cube is calculated using the formula \(6a^2\) with \(a = 8\), leading to \(6 \times (8^2) = 384\) m².

B (48 m squared) YOUR ANSWER

This option reflects a misunderstanding of the surface area formula. It appears to result from calculating the area of just one face of the cube instead of the total surface area. Each face has an area of \(8 \times 8 = 64\) m², and since the cube has 6 faces, the correct total is much larger.

C (2304 m squared) YOUR ANSWER

This choice likely stems from incorrectly applying the surface area formula. It might result from miscalculating \(6 \times (8^3)\) instead of \(6 \times (8^2)\). The volume calculation should not be confused with surface area, which is determined by the square of the edge length.

D (192 m squared) YOUR ANSWER

This option may arise from a miscalculation where one might incorrectly multiply the edge length by the number of faces, leading to confusion. The correct approach is to square the edge length and then multiply by 6, as per the surface area formula, which gives a much different result.

Conclusion

The surface area of a cube is determined by the formula \(6a^2\), which accounts for all six faces. With edges measuring 8 meters, the resulting surface area is 384 m². Misinterpretations of the formula or calculations can lead to incorrect answers, but understanding the correct application ensures accurate results in geometry.

The edges of a cube are 8 meters long. What is the surface area of the cube?

The surface area of the cube is 384 m squared.

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