Final answer:
The mass of the solid gold rectangular bar is calculated using the formula mass = density × volume. After computing the volume in cubic meters and using the density of gold, the mass is found to be 23.35 kg.
Step-by-step explanation:
The question requires us to calculate the mass of a solid gold bar using its volume and the density of gold. The volume (V) of the rectangular bar is found by multiplying its length (l), width (w), and height (h). Then, to find the mass (m), we use the density (d) of gold in the equation m = d × V.
Firstly, we calculate the volume of the gold bar:
- Volume, V = l × w × h
- = 4.40 cm × 13.0 cm × 21.0 cm
- = 1209.6 cm³
Now, convert the volume from cm³ to m³ (since density is given in kg/m³), knowing that 1 cm³ = 1 × 10^-6 m³:
- Volume, V = 1209.6 cm³ × 1 × 10^-6 m³/cm³
- = 0.0012096 m³
Finally, multiply the converted volume by the density of gold to find the mass:
- Mass, m = d × V
- = 19.3 × 10^3 kg/m³ × 0.0012096 m³
- = 23.35 kg
The mass of the solid gold bar is 23.35 kg.