Archie needs to find the volume of a gold crown. He partly fills a container with water and records the height of the water. He then puts the crown in the water and measures the new height of the water. What is the volume of the gold crown?
To find the volume of the gold crown, we can use the principle of displacement. The change in water level when the crown is submerged will give us the volume of the crown.
Here are the steps:
1. Measure the initial height of the water in the container and record it. Let's call it h1.
2. Carefully put the gold crown into the container, ensuring that it is fully submerged.
3. Measure the new height of the water in the container when the crown is submerged and record it. Let's call it h2.
4. The difference between the initial height of the water and the final height of the water (h1 - h2) represents the volume of the crown.
Therefore, the volume of the gold crown is equal to the change in water level, which can be calculated as h1 - h2.
To find the volume of the gold crown, Archie can use the principle of buoyancy.
Buoyancy states that the weight of the water displaced by an immersed object is equal to the weight of the object itself. By measuring the change in water level when the crown is placed in the container, Archie can determine the volume of the crown.
Here's how Archie can determine the volume of the crown:
1. Fill the container with water up to a certain height and record the initial water level. Let's call this "h1".
2. Carefully place the crown into the container, ensuring it is fully immersed in water. The crown should not touch the sides or bottom of the container.
3. Observe the new water level and record it. Let's call this "h2".
4. Calculate the change in water level: Δh = h2 - h1. This represents the increase in water volume due to the crown being submerged.
5. Calculate the volume of the gold crown using the formula V = A * Δh, where A is the cross-sectional area of the crown and Δh is the change in water level.
Keep in mind that for accurate results, it is important to ensure that the crown is fully immersed and no air bubbles are trapped inside it or the container.
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If the crown is totally submerged, then just subtract the old volume of water from the new volume (which includes the crown).