Final answer:
The mass of the gold bar is found using the formula for density: Density = Mass / Volume. After converting the dimensions of the bar to meters and calculating its volume, we can rearrange the formula to find that the mass is about 437.644 kilogram.
Step-by-step explanation:
To find the mass of the gold bar, we will use the formula associated with density: Density = Mass / Volume. The density of gold has been given as 19.3 x 10³ kg/m³. However, the dimensions of the gold bar are given in centimeters, which means that we first need to convert them into meters. Convert by dividing each number by 100. This gives us the dimensions: l = 0.06 m, w = 1.40 m, h = 0.27 m.
Next, we calculate the Volume of the gold bar using the formula for the volume of a rectangular prism, which is: Volume = length * width * height. Substitute l=0.06m, w=1.40m, h=0.27m into the formula to get Volume = 0.06 m * 1.40 m * 0.27 m = 0.02268 m³.
Finally, to determine the Mass, we rearrange the density formula to: Mass = Density * Volume, substitute in the given density of gold and our calculated volume to get Mass = 19.3 x 10³ kg/m³ * 0.02268 m³ = 437.644 kg. Thus, the mass of the gold bar is approximately 437.644 kilogram.
Learn more about Density Formula