The instrument used to measure the volume of an irregular solid is a graduated cylinder and water. Here's how it works:

1. Fill the graduated cylinder with water. Note the initial water level.

2. Carefully submerge the irregular solid in the water. Make sure it's completely submerged.

3. Observe the new water level. The difference between the initial and final water levels represents the volume of the irregular solid.

This method is based on the principle of displacement. The solid displaces an amount of water equal to its own volume.