The density of gold is 19.32 g/cm3. What is the mass of a bar of gold measuring 4.50 cm by 2.50 cm by 6.50 cm?

Question

BlackTom AI · Accepted Answer

We start by identifying the given quantities and the relationship between mass, density, and volume. Density = mass / volume, so mass = density × volume.

Option calculations:
Option 1: 1410 g. To check, compute the bar’s volume: 4.50 cm × 2.50 cm × 6.50 cm = 11.25 cm^2 × 6.50 cm = 73.125 cm^3. Multiply by the density: 19.32 g/cm^3 × 73.125 cm^3 = 1412.775 g, which is very close to 1410 g when rounded to three significant figures. This aligns with the expectation that mass equals density times volume.

Option 2: 500 g. This would imply a volume of 500 g ÷ 19.32 g/cm^3 ≈ 25.87 cm^3, which is far smaller than the actual bar’s volume (73.125 cm^3). Therefore this value is inconsistent with the given dimensions.

Option 3: 3.78 g. This is orders of magnitude too small for the calculated volume at the given density; such a mass would correspond to a volume around 0.195 cm^3, not matching the 73.125 cm^3 volume of the bar.

Option 4: 0.264 g. Similar to Option 3, this mass would require a tiny volume (0.264 g ÷ 19.32 g/cm^3 ≈ 0.0137 cm^3), which contradicts the actual dimensions and volume of the bar.

Synthesis: The correct approach is to compute volume from the provided dimensions, then multiply by the density to obtain mass. The calculated mass ~1412.8 g is best represented by the closest option, 1410 g, while the other options correspond to densities or volumes that do not match the given measurements.

In summary, the steps are: (1) calculate volume from dimensions, (2) multiply by density to get mass, (3) compare to answer choices and select the closest consistent value, (4) recognize why each incorrect option fails to match the physics of density and the bar’s geometry.

The density of gold is 19.32 g/cm3. What is the mass of a bar of gold measuring 4.50 cm by 2.50 cm by 6.50 cm?单项选择题

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