Question

Pure gold has a density of 19.3 g/ml. A gold bracelet has a mass of 412 g and a volume of 22.4ml. Is the bracelet pure gold? Explain.

Answer 1

`\boxed {\boxed {\sf No, \ the\ densities \ aren't \ equal}}`

Step-by-step explanation:

First, let's find the density of the gold bracelet.

Density can be found by dividing the mass by the volume.

`d=(m)/(v)`

The mass of the bracelet is 412 grams and the volume is 22.4 milliliters.

`m=412 \ g\\v= 22.4 \ mL`

Substitute the values into the formula.

`d=(412 \ g)/(22.4 \ mL)`

Divide.

`d=18.3928571 \ g/mL`

Let's round to the nearest hundredth.

• The 2 in the thousandth place tells us to leave the 9 in the hundredth place.

`d \approx 18.39 \ g/mL`

The density of the bracelet is about 18.39 grams per milliliter.

Now, let's compare the bracelet's density to pure gold's density.

`bracelet= 18.39 \ g/mL\\pure \ gold=19.3 \ g/mL`

It's quite clear that the two values are not equal. Therefore, the bracelet cannot be made of pure gold, because it's density doesn't match pure gold's.