Answer: The side length of the cube is 2.27cm
Step-by-step explanation:
The options are not given, then let's solve this in a general way.
We know that the density of gold is 19.3g/cm^3.
We also know that 1 oz = 28.35g.
And we know the relation:
Density = mass/volume.
Now, let's find the volume of 8 ounces of gold.
First, let's rewrite the density changing the units, from grams to ounces.
We know that:
1 oz = 28.35g
(1 oz/28.35g) = 1.
Then if we multiply the density by this ( that is equal to 1) we can change the units and leave the actual quantity invariant.
d = 19.3g/cm^3 = 19.3g/cm^3*(1 oz/28.35g) = 0.68 oz/cm^3
Now let's use the equation for the density, knowing this time that the mass is 8 ounces.
0.68 oz/cm^3 = mass/volume = 8oz/V
Let's find the value of V
0.68 oz/cm^3 = 8oz/V
V = 8oz/0.68 oz/cm^3 = 11.76 cm^3
Now, we know that this is a cube.
Remember that the volume of a cube of side length L is:
V = L^3
Then we have:
L^3 = 11.76 cm^3
L = ∛11.76 cm^3 = 2.27 cm
The side length of the cube is 2.27cm
