A 19.3- gmass of gold in the form of a cube is 1.00 cmlong on each side (somewhat smaller than a sugar cube).What would be the length of the sides of a cube having four times this mass of gold?
Four times the mass of gold would be 19.3 g * 4 = 77.2 g. So, we have a new cube with a mass of 77.2 g.
Now, let's find the length of the sides of this cube. Since the initial cube had a mass of 19.3 g and a side length of 1.00 cm, we can use the ratio of the masses to determine the ratio of the side lengths.
The ratio between the masses is 77.2 g / 19.3 g = 4.
Therefore, the ratio between the side lengths is also 4.
To find the length of the sides of the new cube, we multiply the side length of the initial cube (1.00 cm) by the ratio of the side lengths (4).
This gives us 1.00 cm * 4 = 4.00 cm.
So, the new cube would have a side length of 4.00 cm.
In simpler terms, the cube would be the size of a sugar cube after hitting the gym and bulking up with four times the mass of gold!
To find the length of the sides of a cube with four times the mass of gold, we can use the concept of density. Density is defined as mass divided by volume.
1. First, let's calculate the volume of the initial gold cube. The volume of a cube is given by the formula V = s^3, where s is the length of each side.
Given: Length of each side of the initial gold cube = 1.00 cm
Therefore, the volume of the initial gold cube = (1.00 cm)^3
2. Next, we need to calculate the density of gold using the given mass and volume.
Given: Mass of the initial gold cube = 19.3 g
Density of gold (ρ) = mass/volume
Density of gold = 19.3 g / [(1.00 cm)^3]
3. Now that we have the density of gold, we can use it to calculate the mass of a cube with four times the mass.
Given: Mass of the new gold cube = 4 * mass of the initial gold cube
Mass of the new gold cube = 4 * 19.3 g
4. Lastly, we can use the density and the mass of the new gold cube to calculate the length of each side of the cube.
Given: Density of gold (ρ) = 19.3 g / [(1.00 cm)^3]
Density of gold (ρ) = Mass of the new gold cube / [(Side length of new gold cube)^3]
Rearrange the equation to solve for the side length of the new gold cube:
(Side length of new gold cube)^3 = Mass of the new gold cube / Density of gold
Take the cube root of both sides to find the side length of the new gold cube.
By following these steps, you should be able to determine the length of the sides of a cube having four times the mass of gold.
To find the length of the sides of a cube with four times the mass of gold, we can use the relationship between the mass and the volume of a cube.
Let's start by finding the volume of the original gold cube.
The volume of a cube is given by the formula: V = s^3, where V is the volume and s is the length of its side.
In this case, the length of the side, s = 1.00 cm. So, the volume of the original gold cube is:
V = (1.00 cm)^3 = 1.00 cm^3
Now, we can find the mass density of gold. The density of gold is approximately 19.3 g/cm^3.
The mass of the original gold cube is given as 19.3 g. By rearranging the density formula, we can calculate the original volume of the gold cube using the mass and density:
V = m / ρ
V = 19.3 g / 19.3 g/cm^3
V = 1 cm^3
Since the mass of the gold cube is directly proportional to its volume, increasing the mass four times will result in a cube with four times the volume.
Therefore, the volume of the cube with four times the mass is:
V' = 4 * V
V' = 4 * 1 cm^3
V' = 4 cm^3
To find the length of the sides of the new cube, we need to solve for s:
s^3 = V'
s^3 = 4 cm^3
Taking the cube root of both sides:
s = ∛(4 cm^3)
s ≈ 1.59 cm
Therefore, the length of the sides of the cube with four times the mass of gold is approximately 1.59 cm.