**Volume**

Volume of Cube and Cuboid

Volume: The **Volume** of any
three-dimensional figure refers to the measure of space occupied by any
substance in it.

So, the **Capacity** of any three-dimensional figure refers to
the measure of the substance that the interior of the object can
accommodate.

- The units for measuring volume are cubic units,cm3,m3 etc.
- The units for measuring capacity are litres or millilitres.

Relation Between Cubic Centimetres (CC)and Millilitres and Litres

1Litre = 1000 CC and 1CC = 0.001 L

1Mililitres = 1 CC

Example:

- Convert CC to millilitres and litters: 30 CC
- Convert millilitres and litters to CC: 30 mL and 30 L

Answer:

- 30 CC = 30 mL

30 CC = 0.03 L -
30 mL = 30 CCM

30 L = 30000 CC

Difference Between Volume and Capacity

1. The volume of any three-dimensional solid figure is the measure of space occupied by the solid. | 1. The capacity of any object is equal to the volume of substance that the interior of the object can accommodate. |

2. Both solid and hollow objects have volume. | 2. Only hollow objects have the capacity. |

3. Units of we use for volume is CC, Cubic meter. | 3. Units of we use for capacity are litres or millilitres |

Volume of a Cuboid

The volume of a cuboid is equal to the amount of space occupied by the cuboid. It depends on the three dimensions of the cuboid, which are length, breadth and height.

Formula to find Volume of Cuboid:

Volume of Cuboid = Length Ă— Breadth Ă— Height or, Volume of Cuboid = l Ă— b Ă—
h

when, l = Length

b = Base

h = Height

Steps to find Volume of Cuboid:

To find the volume of the cuboid, we need to know the dimensions of the cuboid first. If all the dimensions are given, then the below steps to follow to find the volume.

**Step 1:** Check the length, breadth and height of the cuboid.

**Step 2:** Check if all units of the length, breadth and
height are the same. If not then convert the length, breadth and height into
the same units.

**Step 3:** Then multiply the length, height and breadth of the
cuboid to find the volume.

**Step 4:** The result of the multiplication is the volume of
the cuboid, written with the cubic unit.

Example:

Find the volume of the cuboid with a length of 5 cm, a width of 2 cm and a height of 3 cm

Answer:

Length = 5 cm, Width = 2 cm, and Height = 3 cm

Volume = (5 Ă— 2 Ă— 3) CC = 30 CC

Hence, the volume of the cuboid is 30 CC.

Volume of a Cube

The volume of a cube refers to the total space occupied by it. It defines the number of cubic units occupied by the cube completely. The volume of the cube depends on its length, breadth and height of the cube.

Formula to find Volume of Cube:

Volume of Cube = Length Ă— Length Ă— Length

or,

Volume of Cube = a Ă— a Ă— a = a3

When, Length = a

Steps to find Volume of Cube:

To find the volume of the cube, we need to know the dimensions of the cube first. If all the dimensions are given, then follow the below steps to find the volume.

**Step 1:** Check the length of the cube.

**Step 2:** Then multiply the length of the cube three times by
itself to find the volume.

**Step 3:** The result of the multiplication is the volume of
the cube, written with the cubic unit.

Example:

Find the volume of the cube with a length of 5 cm.

Answer:

Length = 5 cm

Volume = (5 Ă— 5 Ă— 5) CC = 125 CC

Hence, the volume of the cuboid is 125 CC.