Intro to Mass and Volume

I. Mass

Mass is defined as the amount of matter that an object contains. The SI unit of mass is the kilogram (kg). The kilogram is the only SI base unit that contains a prefix. This is because when the first physical standard for mass was created in 1799, the methods to measure the mass of something as small as a gram did not exist.

Note: The mass of a body is constant; it does not change at any time. Only in certain extreme cases when a huge amount of energy is given or taken from a body, the mass may be impacted. 

There are various units for calculating mass, like, kilograms, grams, pounds, etc., but the SI unit of mass is 'kilogram' or kg. Note: 1kg is equal to 2.20462 pounds.

Kilo = 1000

Therefore

1000 grams = 1 kilogram

Here are some various objects to get a sense of weight in grams and kilograms.

paper clip ≈ 1g

pencil ≈ 5g

mouse ≈ 20g

kitten ≈ 200g - 300g

text book ≈ 1kg

cat ≈ 3kg - 5kg

adult person ≈ 60kg - 80kg

cow ≈ 750kg

Difference Between Mass and Weight

Mass is often confused with the term weight. Weight is a measure of force that is equal to the gravitational pull on an object. The weight of an object is dependent on its location. On the moon, the force due to gravity is about one sixth that of the gravitational force on Earth. Therefore, a given object will weigh six times more on Earth than it does on the moon. Since mass is dependent only on the amount of matter present in an object, mass does not change with location. The difference between mass and weight is shown in the table given below.

	Mass	Weight
Definition	Mass is defined as the amount of matter in a substance	Weight is defined as the amount of force acting on the mass of an object because of acceleration due to gravity.
Denotation	Mass is represented by 'M'	Weight is represented by 'W'
Formula	•Mass is always constant for a body. •One way to calculate mass: Mass = volume × density	•Weight is the measure of the gravitational force acting on a mass. •Formula of weight: Weight = mass × acceleration due to gravity
Unit of Measurement	The SI unit of mass is 'kilogram'	The SI unit of weight is Newton (N).
Quantity Type	•Mass is a base quantity. •Mass only has magnitude and hence, it is a scalar quantity	•Weight is a derived quantity. •Weight has both magnitude and direction (toward the center of gravity) and hence, it is a vector quantity.
Measuring Instrument	Balance scale (comparing known masses).	Spring scale (measuring force/pull)

The confusion between mass and weight largely exists due to how we use these terms in everyday language. When you place a bowl on a kitchen scale to measure out oats or chopped apples, you are performing an action we call "weighing." But your ultimate goal isn't to find out the gravitational pull on those ingredients—you just want to know how much physical stuff is there (the mass) so your recipe turns out right.
Here is what is actually happening inside your kitchen scale:

1. It measures force (Weight): Most modern digital scales do not measure mass directly. Inside the scale is a small electronic component called a load cell (or strain gauge). When you put something on the scale, gravity pulls the item down, slightly bending the load cell. The scale is measuring that physical downward force—technically, it is measuring Newtons. 2. It calculates and displays matter (Mass): Because we need mass for recipes and shipping, the scale's computer chip acts as a translator. It takes the force it just measured and divides it by Earth's standard gravity ($9.81 m/s^2$). It then displays that mathematical result on the screen in grams or kilograms.

II. Volume

Volume is the amount of three-dimensional space that an object occupies. The simplest three dimensional shape is a cuboid.

Previously, we explored how a 1D measurement captures a single linear distance, and how adding a second dimension allows us to calculate 2D flat surface area. Now, we progress to the third dimension: volume. Volume measures the total capacity of a 3D object, telling us exactly how much physical space it occupies.

Calculating Volume

Just as area calculates how many 2D square units cover a flat surface, volume calculates how many 3D cubic units (or units cube) completely fill a space.

Volume of a Cuboid

Suppose we have some rectangular sheets with length 'l' and width 'b'. If we stack them one on top of the other up to height 'h', we get a cuboid of dimensions l, b, h. This can be seen in the following figure which shows the length, width (breadth), and height of the cuboid thus formed.

To calculate the amount of space enclosed by this cuboid, we use the formula: Volume of a Cuboid = l × b × h

Unit of Volume

The S.I. unit of volume is cubic meter (m³) since volume is a quantity of the three-dimensional space occupied by a shape or surface. However, the most commonly used unit for volume is liter.

Milli = 1/1000

Therefor 

1000 milliliter = 1 liter

Here are some things to get a sense of volume in milliliters and liters.

20 drops ≈ 1 ml

teaspoon of water ≈ 5 ml

bottle of milk ≈ 1 l

Olympic size swimming pool ≈ 2,500,000 l

Reference

Cuemath: Mass
Khan: Understanding mas (grams and kilograms)

Cuemath: Volume

Ck12: Mass and Weight