If a cube with edges of 1.000 cm weighs 25.68 g, what would the mass of a cube
of the same material with sides 2.63 cm in length be?
Use cube 1 to determine the density of the material. density = mass/volume. You have the mass and you can calculate the volume.
Now, using the density and the volume of cube 2, determine the mass of cube 2.
Post your work if you get stuck.
Here is my work, but the answer is incorrect.
D = M/V
D = 25.68 g/1.000 cm
D = 25.68 g/cm
That is for cube 1.
Mass = Density * Volume
Mass = 25.68 g/cm * 2.63 cm
Mass = 67.5384 g
This answer is incorrect. What did I do wrong?
To find the mass of a cube with sides of different lengths but the same material, you can use the concept of volume and density.
The volume of a cube is calculated by cubing the length of one side, so the volume of the first cube is (1.000 cm)³ = 1 cm³.
Since the material of both cubes is the same, the density of the material is constant. Density is defined as mass divided by volume.
First, we need to find the mass of the first cube. We are given that it weighs 25.68 grams, so the mass of the first cube is 25.68 g.
Now, we can use the density of the material to find the mass of the second cube. To do this, we need to calculate the volume of the second cube.
The volume of the second cube is (2.63 cm)³ = 18.22 cm³.
Since density is the same for both cubes, and density = mass/volume, we can set up a proportion to find the mass of the second cube:
(25.68 g) / (1 cm³) = (mass of second cube) / (18.22 cm³)
Cross-multiplying gives:
(25.68 g) * (18.22 cm³) = (mass of second cube) * (1 cm³)
Simplifying:
467.5296 g*cm³ = (mass of second cube) * (1 cm³)
Dividing both sides by 1 cm³:
mass of second cube = 467.5296 g
Therefore, the mass of the cube with sides of 2.63 cm in length would be approximately 467.53 grams.