In a land far away, long, long ago, the king sent to the royal goldsmith a five pound ingot of pure gold. "From this gold", commanded the king, "fashion for me a crown". When the crown was presented to the king, he wondered whether the crown was truly pure gold or if the greedy goldsmith had cheated him by replacing part of the gold with copper. The king asked the court chemist to determine, without damaging the crown, whether it did indeed consist of pure gold. The chemist, being a clever soul (aren't they all), weighed the crown and found that it did, in fact, weigh precisely five pounds. The chemist then proceeded to immerse the crown in a flask of water. The flask, which initially contained 1000 mL of water, now appeared to contain 1170 mL of water. Knowing that the density of pure gold is 19.3 g/mL, what did the chemist tell the king?

When the chemist placed the crown in water and measured the difference in volume, he was doing water displacement. He was measuring the volume of the crown. According to his measurements, the crown is 170 mL.

1170 - 1000 = 170

Now that you have the crown's volume, you can use the density of gold to determine the weight. If the crown is made of pure gold, the calculations will prove that the crown is indeed 5 pounds. If the calculations show a value that is greater than 5 pounds, the crown is not pure gold.

170 mL × 19.3 g/mL = 3281 g

3281 g > 2267.96 g

The crown is not made from pure gold.