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 = side^{3}
Hence, a cube has:
(i) six surfaces or faces,
(ii) 8 vertices,
(iii) 12 edges or sides of equal length.
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:
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:
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 cm^{3}
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
● Volume.
5th Grade Geometry
5th Grade Math Problems
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