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Hi everyone. This problem reads a jeweler would like to assess if a ring is made of pure gold. The mass of the ring was measured to be 11.49g to determine the volume. The ring was placed in a graduated cylinder containing 15 ml of water After which the volume increased to 19. ml determine if the ring is made of pure gold. By calculating the ring's density. The density of pure gold is 19.3 g per mil leader. Okay, So our goal with this problem is to calculate the rings density. Okay, so once we calculate the rings density, we're going to compare it to the density of gold which was given at 19.3 g per male leader. When we compare these two numbers, we'll be able to see whether or not this ring is pure gold or not. So, let's start off by Writing our density equation to find out our density of the ring. Okay, so density is equal to mass over volume. Okay, so let's look at the problem. To see what we can plug in. We have the mass of the ring that was given. Were told that the mass is 11.49g. All right, so now we need the volume. Okay, so the volume is we're going to need to calculate this. Okay, so the volume of the ring is going to equal the total volume minus the volume of the water. Okay, Because both of these values were given, but we just need the volume of the ring. Okay, so the total volume is 19.8 mil milliliters. Because we're told in the problem. The ring was placed in a graduated cylinder containing mL milliliters of water after which the volume increased to 19.8. Okay, so that means we need to take 19.8 Male leaders and subtract 15 mil leaders from that, which gives us a volume of 4.8 mil leaders for the volume of the ring. Alright, so let's go ahead and plug that up here. So we have 4.8 mil leaders. Alright, so Now that we have that we can calculate the density of the ring. So our density turns out to be 2.39 g per mil leader. This is the density for the ring. Okay, so now we see that the density of the ring. Okay, is less than let's put this in a different color. The density of the ring is less than 19.3 grams per mil leader, which is the density of pure gold. Okay, so let's write that here. This is the ring and this is pure gold. Okay, so because the density of the ring is less than the density of pure gold, the ring is not pure gold. Okay, so our answer here is going to be be that the ring is not pure gold because it has a less density than pure gold. Alright, so that is the answer to this problem and that's the end of this problem. I hope this was helpful.

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