Question

A pure gold metal bar displaces 0.82 L of water. What is the mass in kilograms? (the density of gold is 19.3 g/cm^3)

Answer 1

The mass of a pure gold bar that displaces 0.82 L of water is 15.826 kg, calculated using the density of gold (19.3 g/cm³) and converting the volume from liters to cubic centimeters.

Step-by-step explanation:

To find the mass of a pure gold bar in kilograms, given that it displaces 0.82 L of water, we need to use the density of gold. The density of gold is given as 19.3 g/cm³. First, we must convert the volume from liters to cubic centimeters (cm³), because the density of gold is given in g/cm³. We know that 1 L = 1000 cm³, so 0.82 L of water will correspond to 0.82 * 1000 cm³ of gold.

Next, we calculate the mass of the gold using the formula:

mass = density × volume

Plugging in the values we get:

mass = 19.3 g/cm³ × 820 cm³

mass = 15826 g

To convert the mass from grams to kilograms we divide by 1000, since 1 kg = 1000 g. Therefore:

mass = 15826 g / 1000

mass = 15.826 kg

The mass of the pure gold bar is 15.826 kilograms.

Answer 2

Mass of gold bar is 15.8 kg

Step-by-step explanation:

The gold metal bar displaces volume of water equal to volume of metal bar.

So, volume of gold metal bar = 0.82 L

`1cm^(3)=0.001L`

We know that density is the ratio of mass to volume.

So mass of gold bar = (density of gold)
`*`(volume of gold bar) = (
`19.3*0.82* (1)/(0.001)`)g =15826 g

Now, 1 g = 0.001 kg

So mass of gold bar = (
`15826* 0.001`) kg = 15.8 kg