LEARNATHON
III

Competition for grade 6 to 10 students! Learn, solve tests and earn prizes!

### Theory:

There is no exact formula to measure irregularly shaped objects, but there are some methods to do it. Since volume is the total space occupied by an object, the volume of a small irregular piece of stone can be found by the water displacement method.
Water displacement method
The volume is determined by using a measuring cylinder, a piece of stone, a thread and water.

Procedure
1. A measuring cylinder with markings is filled with water.
2. From the readings of the measuring cylinder, the volume is taken as $$V_{1}$$.
3. A stone is tied with a piece of thread and immersed fully into the water.
4. The thread is held in such a way that it does not touch the walls of the cylinder.
5. When the stone is immersed, the level of water is increased.
6. Again the readings of the measuring cylinder are noted, and the volume is taken as $$V_{2}$$.
Inference

The stone occupied the space inside the cylinder by displacing some amount of water. This made the water level to rise. Therefore, the volume of water displaced will be equal to the volume of space occupied by the stone in the container. This technique is known as 'the water displacement method' and was found by Archimedes.

Formula

Amount of water displaced by the stone

Assume that the water level was $$30\ ml$$ initially. After immersing a piece of stone, the water level rises to $$40\ ml$$. Then,

Volume of the water displaced $$=$$ $$30\ ml$$ $$-$$ $$40\ ml$$ $$=$$ $$10\ ml$$

In terms of $$cubic$$ $$centimetre$$,

$$1\ ml$$ $$=$$ $$1\ cm^3$$
$$10\ ml$$ $$=$$ $$10\ cm^3$$

Hence, the volume of the stone is found to be $$10\ cm^3$$. The volume of an irregularly shaped object can be calculated using this technique.