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?
To find the length of the sides of a cube with four times the mass of the given cube, we need to use the concept of mass and density.
The given cube has a mass of 19.3 g and a side length of 1.00 cm. In order to find the length of the sides for a cube with four times the mass, we can start by calculating the density of gold.
The density of gold is typically given as 19.3 g/cm³. This means that for every cubic centimeter of gold, it weighs 19.3 grams.
Now, to find the volume of the given cube, we can use the formula:
Volume = (side length)³
For the given cube:
Volume = (1.00 cm)³ = 1.00 cm³
Since density = mass/volume, we can rearrange the formula to solve for volume:
Volume = mass/density
For the given cube:
Volume = 19.3 g / 19.3 g/cm³ = 1.00 cm³
Now, for a cube with four times the mass, the new mass would be:
New mass = 4 * 19.3 g = 77.2 g
To find the length of the sides for this new cube, we can use the formula:
Volume = (side length)³
Now, substitute the values:
77.2 g / 19.3 g/cm³ = (side length)³
Solving for side length:
(side length)³ = 77.2 g / 19.3 g/cm³
(side length)³ = 4 cm³
Taking the cube root of both sides:
side length = ∛(4 cm³)
Calculating the cube root of 4 cm³, we find:
side length ≈ 1.587 cm
Therefore, the length of the sides of a cube with four times the mass of the given gold cube would be approximately 1.587 cm.