Suppose you have two 100-{\rm mL} graduated cylinders. In each cylinder there is 58.5mL of water. You also have two cubes: One is lead, and the other is aluminum. Each cube measures 2.0cm on each side.
After you carefully lower each cube into the water of its own cylinder, what will the new water level be in each of the cylinders? Assume that cubes are totally emerged in the water.
nevermind, I just figured it out
How did you figure it out?
To find the new water level in each cylinder after placing the cubes in them, we need to determine the volume of each cube and then add that volume to the initial water volume.
Let's start with the volume of a cube. A cube has equal sides, so each side measures 2.0 cm. The volume of a cube is calculated by raising the side length to the power of 3, so the volume of each cube is:
Volume of Cube = (Side length)^3 = (2.0 cm)^3
Calculating this, we get:
Volume of Cube = 8.0 cm^3
Since 1 mL is equal to 1 cm^3, the volume of each cube is 8.0 mL.
Now, let's calculate the new water level in each cylinder. Initially, both cylinders contain 58.5 mL of water. After placing the cube in each cylinder, we need to add the volume of the cube to the initial water volume.
For the cylinder with the lead cube:
New Water Level = Initial Water Level + Volume of Cube
New Water Level = 58.5 mL + 8.0 mL
Calculating this, we get:
New Water Level = 66.5 mL
So, the new water level in the cylinder with the lead cube is 66.5 mL.
For the cylinder with the aluminum cube, we do the same calculation:
New Water Level = Initial Water Level + Volume of Cube
New Water Level = 58.5 mL + 8.0 mL
Calculating this, we get:
New Water Level = 66.5 mL
So, the new water level in the cylinder with the aluminum cube is also 66.5 mL.
Therefore, after carefully lowering each cube into the water of its own cylinder, the new water level in each cylinder will be 66.5 mL.