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.

HonNxtGenChem A HNGC Module 1 Practice Quiz #4- Multiplying and Dividing with Significant Figures

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?

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HonNxtGenChem A HNGC Module 1 Practice Quiz #4- Multiplying and Dividing with Significant Figures

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?

查看解析

登录即可查看完整答案

类似问题

​Because freshwater is denser than seawater, seawater floats on top of freshwater.

Question at position 3 The key property that determines whether fluid (air or water) sinks or rises is _________.densitycolorsound

The mass of a metal ball bearing is 0.3062 g and the volume is 0.0270 cm3. What is the density?

Which one of the following substances will float in gasoline, which has a density of 0.66 g/mL?

In 2017, approximately 7.7 x 108 kg polyethylene terephthalate (PET) bottles were collected through recycling programs and sold, either to domestic or foreign markets. If the density of PET is 1350 kg/m3, the volume of PET that was recycled in 2017 was _________ m3.

2. A plastic container has a mass of 62 g and a volume of 44.3 cm3. a. What is the density of the plastic container in g/cm3?

更多留学生实用工具

希望你的学习变得更简单

Because freshwater is denser than seawater, seawater floats on top of freshwater.