Volume of a Cube

A cube is a solid box whose every surface is a square of same area.

Take an empty box with open top in the shape of a cube whose each edge is 2 cm. Now fit cubes of edges 1 cm in it. From the figure it is clear that 8 such cubes will fit in it. So the volume of the box will be equal to the volume of 8 unit cubes together.

Therefore, the volume of the cube = 8 cu cm

Note that 8 = 2 × 2 × 2

Thus, volume of a cube = side × side × side = side³

Hence, a cube has:

(i) six surfaces or faces,

(ii) 8 vertices,

(iii) 12 edges or sides of equal length.

$Volume of a Cube$

Since a cube has all sides equal.

Volume of a cube = (side × side × side) cubic units.

= 1 × 1 × 1 cubic units

Since area = side × side

Volume of a cube = (area × side) cubic units.

Solved examples on volume of a cube:

1. Find the volume of cuboid by counting the number of cubes.

Solution:

$Cuboid Volume$

Solution:

The number of unit cubes are 6, its volume is 6 cu cm.

2. Find the volume of cuboid by counting the number of cubes.

Solution:

$Cuboid Volume Problem$

Solution:

The number of cubes are 12, its volume is 12 cu cm.

3. Find the volume of a cube whose edge is 5 cm long.

Solution:

The length of an edge = 5 cm

Volume of a cube = side of edge × side of edge × side of edge

Volume of a cube = 5 cm × 5 cm × 5 cm

= 125 cu cm

= 125 cm³

4. Find the volume of a cube of side 7 cm.

Solution:

We know, volume of a cube = (side × side × side) cubic units.

Here, side = 7 cm.

= 7 × 7 × 7

= 343

Therefore, volume of a cube = 343 cubic cm.

5. Find the volume of a cube of side 13 cm.

Solution:

We know, volume of a cube = (side × side × side) cubic units.

Here, side = 13 cm.

= 13 × 13 × 13

= 2197

Therefore, volume of a cube = 2197 cubic cm.

6. Find the volume of water that can be contained in a cubical container each of whose edge measure 2 m internally.

Solution:

The internal length of an edge of the container = 2 m

The internal volume of the container = 2 m × 2 m × 2 m = 8 cu m

The volume of water that the container can hold = the internal volume of the container.

Therefore, the required volume of water = 8 cu m.

Questions and Answers on Cube:

1. Find the volume of cubes with each edge measuring:

(i) 5 cm

(ii) 10 m

(iii) 1.1 cm

(iv) 30 mm

(v) 4.3 m

Answers:

(i) 125 cu cm

(ii) 1000 cu m

(iii) 1.331 cu cm

(iv) 2700 mm

(v) 79.507 cu m

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