Mass proportional to volume for same density cubes

Steps:

• Density ρ is identical for X and Y, so mass m = ρ × volume V.
• Volume of cube is side length cubed: V_X = x³, V_Y = y³.
• Given m_X = 2 m_Y, substitute: ρ x³ = 2 ρ y³.
• Simplify: x³ / y³ = 2, so (x/y)³ = 2, x/y = ∛2 ≈ 1.26.

Why A is correct:

• ∛2 equals 1.26 by the cube root definition, directly from the volume formula V = side³ for equal-density solids.

Why the others are wrong:

• B: 1.41 is √2, ratio for 2D areas, not 3D volumes.
• C: 2.00 assumes mass scales linearly with side, ignoring cubic volume.
• D: 8.00 is 2³, the volume ratio, not the side ratio.

Final answer: A