A golden bar of metal (5 centimeters by 18 centimeters by 4 centimeters) being transported by armored car is suspected of being fake, made from a less valuable metal with a thin coating of pure gold. The bar is found to have a mass of 2.7 kilograms. if the specific gravity of gold is 19.3, is the bar fake? Justify your answer.

yes

not fake

To determine if the golden bar is fake or not, we need to calculate its volume and compare it with the expected volume of a solid gold bar with the same dimensions.

To calculate the volume of the golden bar, we multiply the dimensions: length x width x height.

Volume = 5 cm x 18 cm x 4 cm
Volume = 360 cm³

Since the mass of the golden bar is given as 2.7 kilograms, we can convert it to grams by multiplying by 1000:

Mass = 2.7 kg x 1000 g/kg
Mass = 2700 g

Now, we need to use the specific gravity of gold to calculate the expected mass of a solid gold bar with the same volume. The specific gravity of gold is the ratio of its density to the density of water, which is 19.3.

Density of gold = Specific gravity x Density of water

Density of gold = 19.3 x 1000 kg/m³
Density of gold = 19300 kg/m³

To convert the density from kg/m³ to g/cm³, we divide it by 1000:

Density of gold = 19300 g/m³
Density of gold = 19.3 g/cm³

Now, we can calculate the expected mass of a solid gold bar with the same volume:

Mass = Density x Volume

Expected Mass = 19.3 g/cm³ x 360 cm³
Expected Mass = 6948 g

Comparing the expected mass of a solid gold bar (6948 g) with the measured mass of the bar (2700 g), we can conclude that the bar is fake. The measured mass is significantly less than the expected mass, indicating that it is made from a less valuable metal with a thin coating of pure gold.

mass of pure gold would be

5*18*4 cm^3 * 19.3 g/cm^3 = 6948g

so, what do you think?