How Big How Heavy - Unit Conversions

Volume is the measure of how much space an object occupies. Imagine a hollow box; the total amount of space inside that box that can be filled with air or liquid is its volume. We measure this space in cubic units like $cm^3$ or $m^3$.

A cuboid is a 3D shape like a shoebox. Its volume can be visualized by filling it with small cubes that are $1\text{ cm}$ on each side. The number of such cubes that fit inside determines the volume, calculated by multiplying the length, width, and height.

A cube is a special cuboid where the length, width, and height are all equal, like a playing die. To find its volume, you simply multiply the side length by itself three times: $Side \times Side \times Side$.

Weight measures how heavy an object is. For light objects, like a feather or a spoon, we use grams ($g$). For heavier objects, like a sack of rice or a person, we use kilograms ($kg$). There are $1000$ grams in every $1$ kilogram.

Capacity refers specifically to the volume of liquids a container can hold. The standard units are litres ($l$) and millilitres ($ml$). Visualise a large $1\text{ litre}$ water bottle; it contains exactly $1000\text{ ml}$ of liquid.

There is a direct link between volume and capacity: $1\text{ cubic centimetre } (cm^3)$ is exactly equal to $1\text{ millilitre } (ml)$. This means a cube with sides of $1\text{ cm}$ can hold exactly $1\text{ ml}$ of water.

Measuring volume by displacement: If you drop an irregular object, like a stone, into a measuring cylinder filled with water, the water level will rise. The difference between the new level and the old level tells you the volume of the stone.