Do you objects of different density displace more water when set into a tub of water?

Two equal volumes with a different density displace the same amount of water, but either the weight or volume of the fake and pure item must be different.

Pure gold is more dense, so it's volume should be less than an equal weight of a fake.

If the fake has the same volume, it would weigh less.

If the fake has the same weight, it's volume would be greater and thus displace more water.

Archmides knew the density of gold and weight of the crown, but to determine if the crown's density was normal for pure gold or not, he needed to measure the volume. And the crown's shape was so irregular, he couldn't calculate the volume.

The Eureka moment was that he figured out how to find the volume. Putting it in water and measuring how much the water level increased in a beaker, he was able to calculate the volume of the displaced water and therefore the volume of the crown. And then check to see if weight/volume was normal for gold.

And about getting your head around the volume thing:

Objects of equal volume, the way that I see it, ought to displace the exact same amount of water. Yes they should, and do.

Displace Water

The volume of the water is always equal to the volume of the submerged item.

The force exerted on the body water is equal to the weight of weight of water displaced.

Density = Mass/Volume

Weight = Mass x acceleration

More water displaced means the water weights more.

As acceleration is constant more water displaced means the water displaced as more mass in both the water and the crown. Higher mass means higher density. Therefore higher density objects displace more water.

Objects of equal volume will of course displace equal volumes of water provided they are totally immersed.

The Archimidian Principle means that if the weight of an object exceeds the weight of the water which it displaces, it will sink. If on the other hand the object weighs less than the water which it would displace if it were totally immersed it will float. The situation then is that the weight of the object is equalled by the weight of water which it is actually displacing.

a million....mass / quantity = density: 0.692g/cm³ 2....mass / density = quantity: 35g / a million.036g/cm³ = 33.784 cm³ ; observe the cancellation of the grams. we would desire to have some thing performed approximately this guy m w. he's continually giving thumbs all the way down to everybody who does not shop on along with his techniques of calculation. I even have reported him and that i'm waiting for some action. Your and my solutions are impressive yet no longer calculated to his liking, for this reason the thumbs down he's warded to each persons. I even have retaliated and could proceed to attain this as long as he insists that others are incorrect.