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?

what is cube root of 4?

To find the length of the sides of a cube having four times the mass of gold, we can use the concept of density.

Density is defined as the mass of a substance per unit volume. In this case, we can assume that the density of gold remains constant.

Given:
Mass of the original gold cube = 19.3 g
Length of the original gold cube = 1.00 cm

Step 1: Find the density of gold.
Density = Mass / Volume

Since the original gold cube has a mass of 19.3 g and a length of 1.00 cm on each side, the volume can be calculated as:
Volume = Length x Length x Length = 1.00 cm x 1.00 cm x 1.00 cm = 1.00 cm^3

So, the density of gold (ρ) = Mass / Volume = 19.3 g / 1.00 cm^3 = 19.3 g/cm^3

Step 2: Find the new mass of the gold cube.
Given that the new gold cube has four times the mass, we can calculate:
New Mass = 4 x 19.3 g = 77.2 g

Step 3: Find the length of the sides of the new cube.
Using the density formula, we can find the volume of the new cube:
Volume = Mass / Density = 77.2 g / 19.3 g/cm^3 = 4 cm^3

Since the new gold cube has a volume of 4 cm^3, and the sides of a cube are equal, the length of each side can be found by taking the cube root of the volume:
Length = ∛(Volume) = ∛(4 cm^3) ≈ 1.59 cm

Therefore, the length of the sides of a cube having four times the mass of gold is approximately 1.59 cm.

To find the length of the sides of a cube with four times the mass of the given gold cube, we need to use the concept of density.

Density is defined as mass divided by volume. Since we have the mass (19.3 g), we can calculate the volume of the given gold cube.

We know that the given gold cube has a side length of 1.00 cm. The volume of a cube is given by the formula:

Volume = side length^3

Plugging in the values, we get:

Volume = (1.00 cm)^3 = 1.00 cm^3

Now, we can calculate the density:

Density = mass / volume

Density = 19.3 g / 1.00 cm^3 = 19.3 g/cm^3

Since density is constant for a given substance, the density will be the same for a cube with four times the mass. Therefore, we can calculate the volume of this larger cube using the given density.

We want to find the length of the sides of the larger cube, so let's call it "x cm".

The volume of the larger cube will be:

Volume = (length of sides)^3 = x^3 cm^3

We know that this larger cube has four times the mass of the given gold cube, so the mass of the larger cube will be:

Mass = 4 * 19.3 g = 77.2 g

Now, we can calculate the volume of the larger cube using the density:

Volume = mass / density

Plugging in the values, we get:

Volume = 77.2 g / 19.3 g/cm^3 = 4 cm^3

Since the volume of a cube is equal to the length of the sides cubed, we can set up the following equation:

x^3 = 4 cm^3

Now, we solve for x by taking the cube root of both sides:

x = ∛4 cm^3 ≈ 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.