A story of archimedes and the gold crown

So today we're going to talk about density. There is an interesting story about density and a legendary greek scientist Archimedes. Archimedes was a greek scientist. About 2000 years ago there was a king and he wanted a new crown. So he went to the goldsmith and gave him some pure gold and asked him to make a new crown. The goldsmith was a dishonest person. He made him a new crown. King knew that the goldsmith was a dishonest person but he didn't know that he actually did keep some of the gold and replaced it with some cheaper metals. So it would weigh the same but it wasn't the actual gold. So he needed to find out whether this crown is real gold, pure gold or there is some impurity in it. He went to Archimedes and explained him the situation. What should we do? Archimedes thought about it and he had this idea that if we calculate the density of this crown we can easily compare it with the density of pure gold and we will know that there is an impurity in it or not. So he started working on it. First he had to know what kind of formula he should use for density. So he thought about this. This is a bowl of styrofoam. It's very lightweight and here is a bowl of some gold metal which is very heavy. So Archimedes said that the mass per unit volume must be the density. The same mass, the same volume of this bowl is containing a mass of suppose 0.05 kilogram and this same bowl here with the same volume it is containing 5 kilograms of gold. So we have same volume but the mass is different. So Archimedes suggests that if we use density as mass per unit volume we can figure out whether the crown is real pure gold or it's impure. So the first thing they weigh the crown and determined its weight whatever it is. But there is a second problem which is that they didn't know what volume is that. He thought and thought of it. He could only have this solution that he would melt this down, make a cube shape and then determine its volume. But the king didn't allow it. He wanted his crown just like that. So they thought and thought but couldn't get a solution out of it. So Archimedes just gave up. He went to take a bath. So he filled the bathtub and then entered the bathtub. When he entered the bathtub the water rose up and Archimedes said that yes this is it that's how we are going to find the volume. He shouted Eureka! Eureka is a Greek word and it means I found it. So he went out took a beaker or whatever he took some water in it and he put the crown in that water. The water rose up. They concluded the difference of the volume and that's there this is they found the volume of the crown. Now they went to the density formula put the mass here put the volume here and found out the density. They found out that the density of this crown is way less than the actual density of gold. No one told what happened to the dishonest goldsmith or but here's the thing the king was not so happy about it. So I think we can guess what happened to the goldsmith and what Archimedes did was very intelligent and that's how he found gravity density. Yeah some people say that this story is not true but whatever it is it's an interesting story and I wanted to share it with you so I shared it. Now since we know how density started and how we came with density we're going to solve some practice problems so that you will have a nice base for the density and we will also do some advanced problems and yeah so see you.