Suppose you have two 100mL graduated cylinders. In each cylinder, there is 36.0mL of water. You also have two cubes: one is lead, and the other is aluminum. Each cube measures 2.40cm on each side.
Alright! To start, let's understand the given information. We have two 100mL graduated cylinders, and in each cylinder, there is 36.0mL of water. We also have two cubes: one made of lead and the other made of aluminum. Both cubes measure 2.40cm on each side.
Now, let's analyze the problem step by step.
Step 1: Calculate the volume of the cubes.
The volume of a cube can be calculated by multiplying the length of its sides. In this case, both cubes have sides measuring 2.40cm. So, the volume of each cube can be calculated as follows:
Volume of cube = length x width x height = 2.40cm x 2.40cm x 2.40cm = 13.824cm³
Step 2: Convert the volume of the cubes to milliliters.
Since the volume of water in the graduated cylinders is measured in milliliters (mL), we also need to express the volume of the cubes in milliliters. To do this, we need to convert cubic centimeters (cm³) to milliliters (mL).
1 cm³ is equivalent to 1 mL. Therefore, the volume of each cube in milliliters would be 13.824mL.
Step 3: Calculate the total volume after adding each cube.
To find the total volume in each graduated cylinder after adding the cube, we need to add the initial volume of water (36.0mL) and the volume of the cube (13.824mL).
Total volume = Initial volume of water + Volume of cube = 36.0mL + 13.824mL = 49.824mL
Thus, the total volume in each graduated cylinder, after placing each cube, would be 49.824mL.
Remember, we assumed that the cubes were placed completely in the cylinders, without displacing the water. If any water spills out or flows over the cylinders' brims, the calculations may differ.