Hello, and welcome to your physics lesson for today. In this chapter, we are going to explore three important ideas: volume, density, and speed. By the end, you will understand how to measure the space objects occupy, how heavy they are for their size, and how fast they move. Let us begin.
Let us start with volume.
We will start with volume. You already know that matter takes up space. The space occupied by any object is called its volume. Think of a stone dropped into a glass of water — the water level rises because the stone pushes water aside, occupying space. This simple observation tells us something fundamental: every object, whether solid, liquid, or gas, has volume.
The S.I. unit of volume is the cubic metre, written as m³. One cubic metre is the volume of a cube with each side measuring exactly one metre. Since this is quite large for everyday use, we often use a smaller unit: the cubic centimetre, or cm³. One cubic centimetre equals the volume of a tiny cube with one centimetre sides.
Here is how these units relate. Since one metre equals one hundred centimetres, one cubic metre equals one hundred centimetres multiplied by one hundred centimetres multiplied by one hundred centimetres. This equals one million cubic centimetres, or 10⁶ cm³. One cubic metre also equals one thousand litres.
For liquids, we commonly use litres and millilitres. One litre equals exactly one thousand cubic centimetres. One millilitre, written as mL, equals one cubic centimetre. So when you see a medicine bottle labelled five hundred mL, you now know it holds five hundred cubic centimetres of liquid.
How do we actually measure volume? For liquids, we use two main tools: the measuring cylinder and the measuring beaker.
A measuring cylinder is a tall, narrow container with markings in millilitres or cubic centimetres. It is perfect for precise measurements in the laboratory. When you pour liquid into it, you must read the level carefully. Liquids curve at the surface — this curve is called the meniscus. Always read the bottom of this curve, keeping your eye level with the liquid surface.
A measuring beaker is wider, with a handle, and is used when you need to measure out a fixed amount of liquid, like two hundred millilitres of milk from a larger container.
For regular solids like cubes or cuboids, measuring volume is straightforward. You simply measure the length, breadth, and height, then multiply them together. The formula is: volume equals length multiplied by breadth multiplied by height.
Or, V = l × b × h where l is length, b is breadth, and h is height. If these are in metres, the result is in cubic metres.
But what about irregular objects, like a stone or a coin? Here we use a clever method called displacement. When you submerge an object in water, it pushes aside — or displaces — a volume of water exactly equal to its own volume.
Imagine you have a measuring cylinder with sixty millilitres of water. You lower a small stone tied to a thread until it is completely underwater. The water level rises to eighty millilitres. The stone has displaced twenty millilitres of water. Therefore, the volume of the stone is twenty cubic centimetres. Simple and elegant.
Now let us turn to area. While volume measures space in three dimensions, area measures surface in two dimensions. The S.I. unit of area is the square metre, m².
For large areas like fields or towns, we use hectares or square kilometres. One hectare equals ten thousand square metres — imagine a square one hundred metres on each side. For small objects, we use square centimetres or square millimetres.
Regular shapes have straightforward formulas. A rectangle's area is length times breadth. A square's area is side squared.
But irregular shapes, like a leaf or a pebble's shadow, need a different approach. We use graph paper. Place the object on the paper, trace its outline, then count the squares inside. Count complete squares, plus squares that are half or more than half covered. Ignore squares less than half covered. If you count twenty-five squares, and each square is one centimetre by one centimetre, the area is approximately twenty-five square centimetres.
Now we come to one of the most important concepts in this chapter: density. Density helps us understand why some materials feel heavy and others light, even when they are the same size.
Consider this. One kilogram of iron and one kilogram of cotton have the same mass, but the cotton fills a much larger space. Conversely, a small iron cube and an identical wooden cube occupy the same volume, but the iron cube is far heavier.
These observations lead us to a precise definition.
The density of a substance is defined as the mass of a unit volume of that substance.
If a body has mass M and volume V, its density d is given by: density equals mass divided by volume.
Or, d = M/V. Here, M is mass and V is volume. The unit of density will be g cm⁻³ or kg m⁻³ depending on whether you use grams and centimetres or kilograms and metres.
The S.I. unit of density is kilogram per cubic metre, written as kg m⁻³. The C.G.S. unit is gram per cubic centimetre, or g cm⁻³. Remember, one gram per cubic centimetre equals one thousand kilograms per cubic metre.
Let us work through an example. Imagine a piece of iron with a volume of twenty-five cubic centimetres and a mass of one hundred and ninety-five grams. Its density would be one hundred and ninety-five divided by twenty-five, which equals seven point eight g cm⁻³. Converting to S.I. units, this becomes seven thousand eight hundred kg m⁻³.
Density is a characteristic property of a substance. It does not change if you reshape the material or break it into pieces. A small piece of iron and a large block of iron have the same density.
However, density does change with temperature for most substances. When heated, materials usually expand, becoming less dense. Water is unusual: it actually becomes denser as it warms from zero to four degrees Celsius, reaching its maximum density at four degrees Celsius. At this temperature, water has a density of one gram per cubic centimetre or one thousand kilograms per cubic metre. Above four degrees, it behaves normally and expands when heated.
Finally, let us explore speed. We see motion all around us — cars on roads, birds in flight, water flowing in rivers. Speed tells us how fast or slow something moves.
Here is the precise definition.
The distance covered or travelled by a body in unit time is called the speed of the body. This can also be expressed as: speed equals distance divided by time.
If a body travels distance D in time t, its speed v is given by v = D/t. The S.I. unit of speed is m s⁻¹. Another common unit is km h⁻¹. One metre per second equals three point six kilometres per hour, or equivalently, five metres per second equals eighteen kilometres per hour.
From this formula, you can also write: distance equals speed times time, and time equals distance divided by speed.
The S.I. unit of speed is metre per second, written as m s⁻¹. Another common unit is kilometre per hour, written as km h⁻¹. To convert from kilometres per hour to metres per second, divide by three point six. To convert from metres per second to kilometres per hour, multiply by three point six.
Picture two friends racing. One friend runs one hundred metres in twenty seconds. His speed is five metres per second. The other cycles one kilometre in one hundred seconds. Her speed is ten metres per second. Clearly, the cyclist is faster. This is how we compare motions using speed.
Let us quickly recap what we have learned today.
First, volume is the space occupied by an object, measured in cubic metres or cubic centimetres for solids, and litres or millilitres for liquids. Irregular solids are measured by water displacement.
Second, area is surface coverage, measured in square metres. Irregular shapes are estimated using graph paper by counting squares.
Third, density is mass per unit volume, given by d = M/V. The S.I. unit is kg m⁻³, and one gram per cubic centimetre equals one thousand kilograms per cubic metre. Density is a characteristic property of a substance, though it varies with temperature.
Fourth, speed is distance travelled per unit time, given by v = D/t. The S.I. unit is m s⁻¹. From this, distance equals speed multiplied by time, and time equals distance divided by speed.
Fifth, careful measurement technique — reading the meniscus, counting squares properly, or timing accurately — leads to reliable results. Sixth, understanding unit conversions helps you solve problems confidently, whether converting centimetres to metres or kilometres per hour to metres per second.
Physics is all around you. Every time you pour water, lift a bag, or watch a vehicle pass, you are witnessing these principles in action. Keep observing, keep measuring, and keep questioning. Until next time, stay curious and keep learning.