Final answer:
A 4-liter bucket of gold dust, with a density of 19.3 g/cm³, would weigh about 170 pounds and would be too heavy to comfortably hold in one hand.
Step-by-step explanation:
The question is whether a free hand can comfortably hold a 4-liter bucket filled with gold dust, given that gold has a density of 19.3 g/cm³. First, we need to find the mass of the gold dust. To do this, we use the formula density (d) = mass (m) / volume (V), and rearrange it to find mass, m = d × V.
Given the density of gold, d = 19.3 g/cm³, and converting liters to cubic centimeters (1 L = 1000 cm³), the volume of 4 liters of gold is V = 4 × 1000 cm³ = 4000 cm³. Thus, the mass of 4 liters of gold dust is m = 19.3 g/cm³ × 4000 cm³ = 77200 g.
To convert this mass into pounds, we use the conversion factor 1 lb = 454 g. The weight in pounds is 77200 g ÷ 454 g/lb ≈ 170.04 lb.
Hence, a 4-liter bucket of gold dust would weigh about 170 pounds, which is too heavy for a person to comfortably hold in one hand.