A 2.9-kg pile of aluminum ( = 2.70 g/cm3) cans is melted, and then cooled into a solid cube. What is the volume of the cube?
density*volume=mass
you know density,and mass, solve for volume.
I need a number?
20 kilograms.
20 grams.
20 milligrams
20 ounces.
20 grams
To find the volume of the cube, we need to first determine the mass of the aluminum cans and then calculate the volume.
Given:
Mass of aluminum cans = 2.9 kg
Density of aluminum = 2.70 g/cm³ = 2700 kg/m³
Step 1: Convert the mass of the aluminum cans to grams.
1 kg = 1000 g
Therefore, 2.9 kg = 2.9 x 1000 g = 2900 g
Step 2: Calculate the volume using the formula:
Volume = Mass / Density
Volume = 2900 g / 2700 kg/m³
Note: We need to have consistent units, so we convert grams to kilograms.
Volume = 2.9 kg / 2700 kg/m³
Now, divide the mass by the density.
Volume = 0.0010741 m³
Step 3: Calculate the side length of the cube.
Since the cube is a regular shape, all sides are equal. So, we need to find the side length.
Side length = ∛Volume
(cube root of the volume)
Side length = ∛0.0010741 m³
Using a calculator or an online cube root calculator, we find that the cube root of 0.0010741 m³ is approximately 0.1037 m.
Step 4: Calculate the volume of the cube.
Once we have the side length of the cube, we can calculate the volume.
Volume of the cube = (Side length)³
Volume of the cube = (0.1037 m)³
Using a calculator, we find that the volume of the cube is approximately 0.001144 m³.
Therefore, the volume of the cube formed from the melted aluminum cans is approximately 0.001144 cubic meters.