Mass = density × volume
If the density and volume are known, this formula can be used to calculate the mass of matter. On the contrary, if the mass and density of a substance are known, the volume can be calculated by rearranging the formula:
Volume = mass/density
It is a basic physical relationship that density multiplied by volume equals mass, which is often used in science and engineering, such as material measurement, material performance evaluation, material transformation and so on.
Relationship between density and volume
There is a simple relationship between density and volume: density multiplied by volume equals mass.
Mathematically, it can be expressed as:
Density = mass/volume
Can be further transformed into:
Mass = density × volume
This relationship can be deduced from the definition, because density is the ratio of mass to volume of a substance. By dividing the mass by the volume, you can get the mass contained in the unit volume, that is, the density.
On the other hand, if the density and volume of a substance are known, we can calculate the mass of the substance by multiplication. Multiply the density by the volume, you can calculate the mass contained in the unit volume, and then multiply it by the actual volume to get the mass of the whole substance.
The relationship between density and volume is often used in the conversion and calculation between mass, volume and density in science and engineering. It is also the basis for measuring material properties, designing and selecting materials.
Density and volume play an important role in many applications.
1. Identification and classification of materials: By measuring the density of an object, its composition and properties can be judged. Different substances usually have different densities, so density can be used to identify and classify substances, for example, in the fields of ore identification, food analysis and drug quality control.
2. Material selection and design: In engineering and materials science, density and volume are the key parameters for selecting suitable materials. Considering the weight of materials and the size of occupied space, materials with appropriate density and volume are usually preferred to meet specific performance requirements.
3. Buoyancy and buoyancy balance: According to Archimedes principle, the buoyancy of an object in a liquid is related to its volume and the density of the liquid. By measuring the volume of the object and the density of the liquid, we can calculate the buoyancy and judge whether the object will float on the surface of the liquid.
4. Liquid volume measurement: The relationship between density and volume can be used to measure the volume of liquid. By measuring the mass and density of liquid, the volume of liquid can be calculated, which is very useful for laboratory, chemical industry and liquid storage.
5. Engineering calculation and design: In the engineering field, density and volume are used to estimate the mass of objects, calculate the capacity or storage space of materials, and optimize design parameters. For example, in building engineering, the density and volume of materials need to be considered to determine the strength and stability of the structure.
Speaking of examples of density and volume, we can consider the following examples:
Example 1: The volume of an iron block is 500 cm? , the mass is 800 grams. Calculate the density of iron.
Answer: According to the definition of density, density is equal to mass divided by volume. Substitute the known value into the formula, density = 800g/500 cm? = 1.6 g/cm? .
Example 2: The density of an object is 2.5 g/cm? , volume 300 cm? . Calculate the mass of an object.
Answer: According to the definition of density, the mass can be calculated by multiplying the density by the volume. Substitute the known value into the formula, mass = 2.5 g/cm? × 300 cm？ = 750 grams.
Example 3: The density of a piece of wood is 0.8 g/cm? , the mass is160g. Calculate the volume of this block.
Answer: According to the definition of density, the volume can be calculated by dividing the mass by the density. Substituting the known value into the formula, we get the volume = 160g/0.8 g/cm? = 200 cm？ .
These examples can help us understand the relationship between density and volume, and use the definitions of density and volume to solve related calculation problems. Please note that for different units, unit conversion may be required to ensure consistent units are used in the calculation.