Answer:
1.28 cm
Explanation:
Density (ρ) is an intensive property resulting from the quotient of mass (m) and volume (V).
The density of Al is ρAl = 2.70 × 10³ kg/m³
The density of Fe is ρFe = 7.86 × 10³ kg/m³
A Fe sphere of radius 1.82 cm has the following volume.
V = 4/3 × π × r³
V = 4/3 × π × (0.0182 cm)³
V = 2.53 × 10⁻⁵ m³
The mass corresponding to this sphere is:
2.53 × 10⁻⁵ m³ × 2.70 × 10³ kg/m³ = 0.0683 kg
The Al sphere has the same mass, so its volume is:
0.0683 kg × (1 m³/7.86 × 10³ kg) = 8.69 × 10⁻⁶ m³
The radius corresponding to an Al sphere of 8.69 × 10⁻⁶ m³ is:
V = 4/3 × π × r³
8.69 × 10⁻⁶ m³ = 4/3 × π × r³
r = 0.0128 m = 1.28 cm
