Each edge of a metallic cube of mass 5.580 kg is measured as 9.0 cm. Express its density as X × 10³ kg·m⁻³, retaining the correct number of significant figures. What is X?
Options

Question

Each edge of a metallic cube of mass 5.580 kg is measured as 9.0 cm. Express its density as X × 10³ kg·m⁻³, retaining the correct number of significant figures. What is X?

G1 Physics · Accepted Answer

Step 1: Convert edge to metres: a = 9.0 cm = 9.0 × 10⁻² m. Step 2: Cube volume V = a³ = (9.0 × 10⁻²)³ = 7.29 × 10⁻⁴ m³. Step 3: Density ρ = m/V = 5.580/(7.29 × 10⁻⁴) = 7.654 × 10³ kg·m⁻³. Step 4: The edge 9.0 cm has only two significant figures, which limits the reported density to two significant figures. Step 5: Round 7.654 to 7.7. Final answer: X = 7.7 (Option B).