Suppose you have two 100-mL graduated cylinders. In each cylinder, there is 40.0 mL of water. You also have two cubes: one is lead, and the other is aluminum. Each cube measures 1.8 cm on each side. After you carefully lower each cube into the water of its own cylinder, what will the new water level be in the cylinder with lead/aluminum cube?
volume Pb cube = 1.8^3 = ?
volume Al cube = 1.8*3 = ?
The water level in the graduated cylinders will rise. The new water level in each beaker will be the old water level + the volume occupied by each metal.
To determine the new water level in each cylinder after placing the lead or aluminum cube, we need to calculate the volume of each cube and then find out how much water is displaced by each cube.
Step 1: Calculate the volume of the cube
The volume of a cube can be found by cubing the length of one side. In this case, the length of each side is given as 1.8 cm.
Volume of cube = side length^3
Volume of cube = (1.8 cm)^3
Volume of cube = 5.832 cm^3
Step 2: Determine the water displaced by each cube
The water displaced by each cube is equal to the volume of each cube. Since the water level initially is 40.0 mL in both cylinders, this is the same volume of water displaced.
Water displaced by each cube = Volume of cube
Water displaced by each cube = 5.832 cm^3
Step 3: Calculate the new water level in each cylinder
To find the new water level in each cylinder, we need to add the volume of water displaced by each cube to the initial water level.
New water level = Initial water level + Water displaced by cube
For the lead cube:
New water level in cylinder with lead cube = 40.0 mL + 5.832 cm^3
For the aluminum cube:
New water level in cylinder with aluminum cube = 40.0 mL + 5.832 cm^3
Note: To compare volumes accurately, we should convert cm^3 to mL since 1 cm^3 is equivalent to 1 mL.
The new water level in each cylinder will be equal to the initial 40.0 mL plus the volume of each cube, which is approximately 45.832 mL.