Take one empty crate with open top in the form of a cube whoseeach sheet is 2 cm. Now fit cubes of edge 1 cm in it. Indigenous the figure it isclear that 8 such cubes will certainly fit in it. Therefore the volume of the box will it is in equalto the volume of 8 unit cubes together.

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Therefore, the volume that the cube = 8 cu cm

Note the 8 = 2 × 2 × 2

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


Hence, a cube has:

(i) 6 surfaces or faces,(ii) 8 vertices,(iii) 12 edge or political parties of same length.


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Since a cube has all political parties equal.Volume of a cube = (side × next × side) cubic units.= 1 × 1 × 1 cubic unitsSince area = next × sideVolume of a cube = (area × side) cubic units.

Solved examples on volume the a cube:

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

Solution:


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Solution: 

The variety of unit cubes space 6, that is volume is 6 cu cm.

2. Find the volume that cuboid by counting the variety of cubes.

Solution:


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Solution:

The variety of cubes space 12, that volume is 12 cu cm.

3. discover the volume of a cube who edge is 5 cm long.

Solution: 

The length of an sheet = 5 cm

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

Volume of a cube = 5 centimeter × 5 cm × 5 cm

                          = 125 cu cm

                          = 125 cm3

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

Solution: 

We know, volume the a cube = (side × next × side) cubic units.Here, next = 7 cm.               = 7 × 7 × 7                = 343Therefore, volume of a cube = 343 cubic cm.

5. find the volume the a cube of next 13 cm.

Solution: 

we know, volume the a cube = (side × side × side) cubic units.Here, next = 13 cm.                = 13 × 13 × 13                = 2197Therefore, volume of a cube = 2197 cubic cm.

6. discover the volume that water that have the right to be contained in a cubical container every of whose edge measure up 2 m internally.

Solution: 

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

The inner volume that the container = 2 m × 2 m × 2 m = 8 cu m

The volume of water the the container have the right to hold = the internal volume that the container.

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

Questions and Answers on Cube:

1. Uncover the volume of cubes with each sheet 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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