To find the surface area of a cube, you can use the formula:
\[ \text{Surface Area} = 6s^2 \]
where \( s \) is the length of one side of the cube.
From the options provided, we can determine the volume of the cube by checking which answer could correspond to a plausible side length.
-
512 cm²:
- Setting \( 6s^2 = 512 \)
- \( s^2 = \frac{512}{6} \approx 85.33 \) (not a perfect square)
-
384 cm²:
- Setting \( 6s^2 = 384 \)
- \( s^2 = \frac{384}{6} = 64 \)
- \( s = 8 \) cm
-
256 cm²:
- Setting \( 6s^2 = 256 \)
- \( s^2 = \frac{256}{6} \approx 42.67 \) (not a perfect square)
-
36 cm²:
- Setting \( 6s^2 = 36 \)
- \( s^2 = \frac{36}{6} = 6 \)
- \( s \approx 2.45 \) cm (not practical for simple geometry)
From these calculations, 384 cm² is the only valid answer because it corresponds to a cube with side length \( s = 8 \) cm.
So, the surface area of the cube is \( 384 cm² \).