Given that the objects all have the same mass, the object with the smallest volume will have the highest density. This is because density is defined as mass per unit volume, and for a fixed mass, the density is inversely proportional to the volume of the object.
Let's look at the given volumes:
- Object 1: [tex]\(6 \, \text{cm}^3\)[/tex]
- Object 2: [tex]\(8 \, \text{cm}^3\)[/tex]
- Object 3: [tex]\(3 \, \text{cm}^3\)[/tex]
- Object 4: [tex]\(14 \, \text{cm}^3\)[/tex]
To find which object is the most dense, we need to identify the object with the smallest volume.
Here are the volumes in order from smallest to largest:
- Object 3: [tex]\(3 \, \text{cm}^3\)[/tex]
- Object 1: [tex]\(6 \, \text{cm}^3\)[/tex]
- Object 2: [tex]\(8 \, \text{cm}^3\)[/tex]
- Object 4: [tex]\(14 \, \text{cm}^3\)[/tex]
The smallest volume is [tex]\(3 \, \text{cm}^3\)[/tex] which belongs to Object 3.
Therefore, since all objects have the same mass, the object with the smallest volume, which is Object 3, is the most dense. So the answer is:
Object 3
