To find the mass of the gold rod, we first need to calculate its volume. The rod is cylindrical, so we use the formula for the volume of a cylinder:
Volume = π × (radius)² × height
Given the diameter is 4.20 cm, the radius (r) is half of that, which is 2.10 cm. The height (h) of the rod is 8.0 cm.
Plugging in the values:
Volume = π × (2.10 cm)² × 8.0 cm
Volume ≈ 3.1416 × 4.41 cm² × 8.0 cm
Volume ≈ 110.85 cm³
Now, we use the density of gold to find the mass. The density of gold is given as 19.3 g/cm³.
Mass = Density × Volume
Mass = 19.3 g/cm³ × 110.85 cm³
Mass ≈ 2140.4 g
So, the mass of the gold rod is approximately 2140.4 grams.