When measuring an object, we can relate it to different quantities. Understand greatness as everything that can be measured. The focus of this text is to show the possible relationships between the quantities mass, volume and capacity. However, let's go into some details first:
Volume
Fundamental unit: cubic meter (m3);
multiples: They are used for larger and more extensive bodies or objects. The multiples of the cubic meter are: cubic kilometer (km3), cubic hectometer (hm3) and cubic decameter (dam3);
submultiples: They are used for smaller and less extensive bodies or objects. The cubic meter submultiples are: cubic decimeter (dm3), cubic centimeter (cm3) and cubic millimeter (mm3);
Utility: Volume determines the space occupied by a body or object. It can be calculated using the formula: Volume = Length x Height x Width.
Pasta
Fundamental unit: gram (g)
multiples: We use it to indicate the amount of mass of larger bodies or objects. The multiples of the mass measure are: kilogram (kg), hectogram (hg) and decagram (dag).
submultiples: They are used to indicate the amount of mass of smaller bodies or objects. The submultiples of the mass measure are: decigram (dg), centigram (cg) and milligram (mg).
Utility: Mass is used to measure the amount of matter in a body.
Capacity
Fundamental unit: liter (l)
multiples: are used to measure large amounts of volume. Are multiples of the liter:
kiloliter (kl), hectoliter (hl) and dekaliter (dal).
submultiples: are used to measure small amounts of volume. They are sub-multiples of the liter: deciliter (dl), centiliter (cl) and milliliter (ml).
Utility: We use the ability to know the internal volume of a container. The amount of liquid inside the container is equal to its internal volume.
It is possible to relate mass, volume and water capacity through the equivalences described below:
1 dm3 (cubic decimeter) is equivalent to 1 liter (liter) → 1 dm3 = 1 l
1 l (liter) is equivalent to 1 kg (kilogram) → 1 l = 1 kg
1 dm3 (cubic decimeter) is equivalent to 1 kg (kilogram) → 1 dm3 = 1 kg
The reciprocal between these relationships is also valid, that is:
1 liter (liter) is equivalent to 1 dm3 (cubic decimeter)→ 1 l = 1 dm3
1 kg (kilogram) is equivalent to 1 l (liter) → 1 kg = 1 l
1 kg (kilogram) is equivalent to 1 dm3 (cubic decimeter) → 1 kg = 1 dm3
For a better explanation of these relationships, see the image below:
Let's solve two examples so that you can better understand how these three quantities can be used.
EXAMPLES:
1º) The cube in the following image is massive. Considering its dimensions, calculate the volume and mass.
Making the product of the three dimensions of the cube, we obtain its volume:
Volume = length x height x width
V = c. H. there
V = 5 cm. 5 cm. 5 cm
V = (5 cm)3
V = 125 cm3
Now that we know the volume, we must transform 125 cm3 in dm3. Look:
125 cm3: 1000 = 0.125 dm3
like 1 dm3 = 1kg, so 0.125 dm3 = 0.125 kg.
The volume of the massive cube is 125 cm3 = 0.125 dm3. The cube's mass is 0.125 kg.
2) Carla traveled to the Northeast. As the climate in this region is very hot, she needed to drink plenty of fluids to avoid dehydration. Because she is very fond of watermelon, she decided to drink at least 1 jar of this juice a day. Suppose there were 1200 ml of juice in the jar, find out how much this value is in liters and then make the necessary conversions for volume and mass. The volume must be found in m³.
Initially we must convert 1200 ml to liters:
1200 ml: 1000 = 1.2 l (liter)
The exercise asked us to also find the volume and mass of this jug of juice. In the relationships between volume, capacity and mass, we have that: 1 l (liter) is equivalent to 1 dm3 (cubic decimeter). Therefore, 1.2 l (liters) = 1.2 dm3 (cubic decimeter).
let's transform 1.2 dm3 in cubic meters:
1.2 dm3 : 1000 = 0.0012 m3
The mass of this juice in grams is given by the following transformation: 1.2 dm3 = 1.2 kg.
We conclude, therefore, that 1200 ml of juice is equivalent to: 1.2 l (liter), 1.2 kg (kilogram) and 0.0012 m3 (cubic meters).
By Naysa Oliveira
Graduated in Mathematics
