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A piece of metal weighs 9.25 g in air, 8.20 g in water, and 8.36 g when immersed in gasoline.a) What is the density of the metal?

Question

A piece of metal weighs 9.25 g in air, 8.20 g in water, and 8.36 g when immersed in gasoline.a) What is the density of the metal?

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Solution

To find the density of the metal, we need to use the formula for density which is mass/volume. However, we don't have the volume directly, but we can find it using Archimedes' principle which states that the buoyant force on an object is equal to the weight of the fluid displaced by the object.

Step 1: Find the volume of the metal The weight of the metal in air minus its weight in water gives the weight of the water displaced by the metal, which is equal to the volume of the metal (since the density of water is 1 g/cm³). So, the volume of the metal is 9.25 g - 8.20 g = 1.05 cm³.

Step 2: Calculate the density of the metal Now we can find the density of the metal by dividing its mass by its volume. So, the density is 9.25 g / 1.05 cm³ = 8.81 g/cm³.

So, the density of the metal is 8.81 g/cm³.

This problem has been solved

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