Ever wondered what "1 cm of rain" means or why that depth seems to be puny, but you have flood on the streets of the city of endless joy? Even though it may seem strange and non-intuitive the depth (a one-dimensional measurement) actually "intended to imply" a volume (a three-dimensional measurement) when multiplied by an area (any amount).
When someone says it rained 1 cm, they are referring to the depth of the rainfall over a flat, impermeable surface. It means that if you had an open container covering an area, the depth of the water collected at the bottom would be 1 cm. To convert this depth to volume for a specific area, you'd multiply the depth of the rainfall by that area, and here's the main part, it can be any area, including city calcutta or just a bucket or even your mouth.
For example, if you want to know how much rain fell over a square meter area:
1 cm × 100 cm × 100 cm = 10,000 cc, or 10 liters of water. So, for every square meter, 1 cm of rain would equate to 10 liters of water. If we take calcutta to be 206.1 km² then that's 2.061×10^9 liters.
That's over a billion 2-liter bottles full of water from just 1 cm of rainfall over the city. It's a powerful way to visualize the immense volume of water involved in seemingly small amount (in depth) of rainfall over large areas!
If it's your mouth assuming the opening to be say 20 cm² that's only 20 cc of water in your mouth from that same 1 cm rain.
Another example is a parsec. It's a great example of using basic geometry (triangulation) to determine vast interstellar distances, using the easily relatable concept of angle measurements.
When observing a nearby star from Earth, astronomers will notice a tiny shift in its apparent position as Earth orbits the Sun. This shift is called the star's parallax. If the parallax angle is exactly one arcsecond (1/3600 of a degree), the star is said to be at a distance of one parsec from Earth.
To give you a sense of scale:
1 parsec ≈ 3.26 light-years or about 3.086 × 10^13 kilometers.
