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Cube:
Cube is a special type of cuboid whose length, breadth and height are all equal.
Volume of a cube:
Let \(a\) be the edge length of the cube.
Volume of a cuboid \(=\) \(lbh\) cu. units.
For a cube, length \(=\) breadth \(=\) height \(=\) edge
That is, \(l\) \(=\) \(b\) \(=\) \(h\) \(=\) \(a\)
Substitute this in the volume of a cuboid formula.
Volume of a cuboid \(=\) \(a \times a \times a\) \(=\) \(a^3\) \(=\) Volume of a cube
Therefore, the volume of a cube \(=\) \(a^3\) cu. units.
Example:
The edge of the cubical tank is \(5\) \(m\). Find how much water it holds in litres?
\([\)Hint: \(1 \ m^3 = 1000 \ l]\)
Solution:
Edge of the cubical tank \(=\) \(5\) \(m\)
Volume of the cubical tank \(=\) \(a^3\)
\(=\) \(5^3\)
\(=\) \(5 \times 5 \times 5\)
\(=\) \(125\) \(m^3\)
Now, convert \(m^3\) to \(l\).
\(1 \ m^3 = 1000 \ l\)
\(125 \ m^3 = 125 \times 1000 = 125000\)
Therefore, the volume of the cubical tank is \(125000 \ l\).
Important!
For any two cubes:
1. \(\text{Ratio of surface areas}\) \(=\) \((\text{Ratio of sides})^2\)
2. \(\text{Ratio of volumes}\) \(=\) \((\text{Ratio of sides})^3\)
3. \((\text{Ratio of surface areas})^3\) \(=\) \((\text{Ratio of volumes})^2\)
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