Volume
To calculate densityA measure of compactness and the ratio of mass to volume. It is usually measured in kilograms per metre cubed (kg/m3) or grams per centimetre cubed (g/cm3)., the volumeThe volume of a three-dimensional shape is a measure of the amount of space or capacity it occupies, eg an average can of fizzy drink has a volume of 330 ml. of the material must be known. If the object is a regular shape, the volume can be found by using a ruler and one of the equations below.
| Shape | Measurements | Equation |
| cube | length (l), width (w), height (h) | \(lwh\) |
| sphere | diameter (d) | \(\frac {4}{3} \pi (\frac{d}{2})^3\) |
| cylinder | diameter of base (d), length of cylinder (I) | \(\pi(\frac{d}{2})^2~l\) |
| cone | diameter of base (d), length of cylinder (I) | \(\pi (\frac{d}{2})^2~\frac{l}{3}\) |
| Shape | cube |
|---|---|
| Measurements | length (l), width (w), height (h) |
| Equation | \(lwh\) |
| Shape | sphere |
|---|---|
| Measurements | diameter (d) |
| Equation | \(\frac {4}{3} \pi (\frac{d}{2})^3\) |
| Shape | cylinder |
|---|---|
| Measurements | diameter of base (d), length of cylinder (I) |
| Equation | \(\pi(\frac{d}{2})^2~l\) |
| Shape | cone |
|---|---|
| Measurements | diameter of base (d), length of cylinder (I) |
| Equation | \(\pi (\frac{d}{2})^2~\frac{l}{3}\) |
If the object has an irregular shapeA shape with unequal side lengths., the volume can be measured using a displacement canA piece of equipment to measure the volume of an irregular solid. The can is filled with water up to a narrow spout and the solid placed in the can. The water displaced through the spout is collected and its volume measured - this is equal to the volume of the solid. .
The displacement can is filled with water above a narrow spoutA tube or lip that allows liquid to flow or pour from a container. and allowed to drain until the water is level with the bottom of the spout.
As the irregular object is lowered into the displacement can, the water level rises. All the displaced water comes out of the spout and is collected in a measuring cylinderA piece of equipment used to measure the volume of a liquid..
The displacedMoved out of position. For example, an object placed in beaker of water displaces the water, causing the water level to rise. water in the cylinder occupies the same amount of space as the object in the can, which means that their volumes are the same.