The density of gold is 1.93×104 {\rm{kg/m}}^{\rm{3}}. 205 {\rm g} of gold is shaped into a cube.
whats the length of an edge
To find the length of an edge of the cube, we can use the formula for the volume of a cube:
Volume = side length^3
We know that the mass of the gold cube is 205 g. First, we need to convert the mass to kilograms by dividing it by 1000:
Mass = 205 g ÷ 1000 = 0.205 kg
Next, we can use the density of gold and the mass of the cube to find its volume:
Density = Mass / Volume
Rearranging the formula, we can solve for the volume:
Volume = Mass / Density
Plugging in the values, we get:
Volume = 0.205 kg / (1.93 × 10^4 kg/m^3)
By simplifying the calculation, we find:
Volume ≈ 1.062 × 10^-5 m^3
Since the cube has equal side lengths, we can find the length of an edge by taking the cube root of the volume:
Side length = ∛(Volume)
Calculating it, we get:
Side length ≈ ∛(1.062 × 10^-5) ≈ 0.021 m
Therefore, the length of an edge of the gold cube is approximately 0.021 meters.