Final answer:
The cube with a volume of 6m³ has a side length of approximately 1.817m and a rational surface area of approximately 19.806m².
Step-by-step explanation:
If a cube has a volume of 6m³, we first need to determine the length of one side of the cube. The volume of a cube is calculated using the formula V = s³, where V is the volume and s is the length of one side of the cube. To find s, we take the cube root of the volume:
s = ∛V = ∛6m³ ≈ 1.817m
Next, we can calculate the surface area using the formula SA = 6s². Plugging in s, we get:
SA = 6(1.817m)² ≈ 6(3.301m²) ≈ 19.806m²
Since the surface area is the sum of the areas of the six equal squares that make up the faces of the cube, and each of these squares has a rational area (as the side length squared is a rational number), the total surface area of the cube is also rational. Therefore, the surface area of a cube with a volume of 6m³ is a rational number.