## -v-Volume

### Measuring Volume.

** Volume** is

*the space occupied by a body.*The SI unit of volume is **m ^{3}**

### A- Volume of regularly Shaped Objects

Volume of some of the regular solids can be calculated using the formulae given in the following table.

Object |
Volume(formula) |

Cube |
(length)^{3} = L^{3} |

Cuboid |
length X breadth X height = L x b x h |

Cylinder |
pi x radius^{2} x height = pi r^{2} h |

Sphere |
4/3 x pi x (radius)^{3} = 4/3 pi r^{3} |

Cone |
1/3 x pi x (radius)^{2} x height = 1/3 pi r^{2} h |

### Note:-

The solid shape must be hard to be measured accurately; if it is made up of clay or something similar will the calculated volume will not be the true volume.

### B- Volume of Irregularly Shaped Objects

Volume of irregularly shaped objects can be found out by

**i- ****Displacement method.**

By measuring the volume of displaced liquid by an object. We can find the volume of these solids with the help of a measuring cylinder.

** **

**Steps:-**

**a- **Fill the overflow vessel with water until the water start overflowing.

**b- **When water stops overflowing, place the measuring cylinder below the overflowing tube.

**c- **Slowly lower the irregular solid into the water by a very thin string.

**d- **When the water stops overflowing, read the volume of the water collected in the measuring cylinder.

**e- **This reading will be the volume of the irregular solid shape.

**i- ****Measuring cylinder.**

** **To measure the volume of an irregular body using *measuring cylinder*

* ***Steps:-**

**a- **Pour water into a clean measuring cylinder (nearly three fourth of its volume) and record the level of water (v_{1}).

**b- **Slowly lower the irregular solid into the water by a very thin string.

**c- **Measure the new volume of the water and the stone (v_{2}).

**d- **Then calculate the volume of irregular solid shape as

**“v= v _{2}-v_{1}”**

The volume of this stone = ………….

ALSO……

you can use measuring cylinder for sure to measure the volume of liquids.

** **

**Notice that:-**

- The measuring cylinder must be placed on a horizontal bench.
- Using large measuring cylinder to measure small amounts, leads to errors in results.
- You have to avoid parallax error.
- If the string holding the stone is thick it may cause a reading error or absorb little amount of water.
- Equal masses of different densities have different volumes

### Liquid levels

- Reading must be taken at the lowest level of meniscus or curved surface of the liquid.
- Reading must be taken at the top level of meniscus or curved surface of the liquid in case of Mercury.
- Liquid A is water and liquid B is mercury.