A cube A cube whose volume is 1 by 1 cubic centimetre is placed on a cube whose volume is 1 cubic centimetre the two cubes are then placed on the top of a third cube whose volume is 8 cubic CM
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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.
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 a cube whose edge is 5 cm long.
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
2. Find the volume of a cube of side 7 cm.
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.
3. Find the volume of a cube of side 13 cm.
We know, volume of a cube =(side × side × side) cubic units.
Answer:
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