Understanding Density of a Cube: A Practical Example and Conversion

Density is a fundamental concept in physics and engineering, describing the mass per unit volume of a substance. Let us explore the density of a cube with a side length of 5 cm and a mass of 250 grams, step-by-step. This article will guide you through the process of determining the density and converting the units to kg/m3, which is a common unit of density in scientific literature.

Calculating Density Using Basic Formulas

To find the density of the cube, we will use the formula:

Density Mass / Volume

Step 1: Calculate the Volume of the Cube

The volume (V) of a cube with side length (s) is given by the formula:

V s3

For a cube with a side length of 5 cm:

V 5 cm × 5 cm × 5 cm 125 cm3

Step 2: Use the Mass of the Cube

The mass (M) of the cube is given as 250 grams. Now, we can calculate the density (D) as follows:

D M / V

D 250 grams / 125 cm3 2 grams/cm3

Therefore, the density of the cube is 2 grams/cm3.

Converting Density to kg/m3

Often, density is expressed in kg/m3 (kilograms per cubic meter), a common unit in scientific and engineering contexts.

Step 1: Convert Mass from Grams to Kilograms

1 kilogram (kg) 1000 grams (g)

250 grams 0.25 kilograms

Step 2: Convert Volume from cm3 to m3

1 meter (m) 100 centimeters (cm)

1 meter3 (m3) 100 cm × 100 cm × 100 cm 1,000,000 cm3

Therefore, 125 cm3 125 / 1,000,000 m3 1.25 × 10-4 m3

Step 3: Calculate the Density in kg/m3

Density (D) 0.25 kg / 1.25 × 10-4 m3 2000 kg/m3

Thus, the density of the cube in kg/m3 is 2000 kg/m3. This is twice the density of water, which has a density of approximately 1000 kg/m3.

A Note on Units and Expressions

When expressing measurements, it is crucial to use spaces between the numbers and the units. For example:

5 cm (not 5cm) 250 g (not 250g) 1000 m3 (not 1000m3) 125 cm3 (not 125cm3) 1.25 × 10-4 m3 (not 1.25×10^-4 m3)

This ensures clarity and avoids possible misinterpretations in scientific and engineering contexts.