# What are the length of the side of a cube and the volume if the mass of the cube is 50g?the density of the material of cube is 7.8g/cm^3

justaguide | College Teacher | (Level 2) Distinguished Educator

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The density of an object is given by density = mass/volume.

Let the side of the cube be S.

The volume of a cube of side S = S^3

The mass is 50 g and density is 7.8 g/cm^3

Using the information provided we can create an equation:

7.8 = 50/S^3

=> S^3 = 50/7.8 = 6.410 cm^3

The volume of the cube is 6.41 cm^3

S = (50/7.8)^(1/3) = 1.857 cm

The length of the side of the cube is 1.857 cm and the volume is 6.41 cm^3.

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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Since to determine the length of each side of the cube, we need to know the volume, we'll begin by calculating the volume.

First, we'll recall the volume formula:

V = mass/density

From enunciation, we know the mass and the density of material, therefore we can calculate the volume of the cube:

V = 50 g/7.8 g/cm^3

V = 6.410 cm^3

We'll recall the formula that gives the volume of a cube:

V = l^3, where l is the length of the side of the cube.

6.410 = l^3

l = cube root (6.410)

l = 1.857 cm

The requested length of the side of the cube and the volume of the cube are: l = 1.857 cm and V = 6.410 cm^3.