Solids: The bodies occupying space are called Solids. Solids could come in all shapes and sizes. Common ones could be cube, cuboid, cones, sphere, etc.

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Volume of a solid: The space occupied by a solid body is called its volume. The units of volume are cubic centimeter or $latex cm^3 &s=1$ or cubic meters or $latex m^3 &s=1$

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Cuboid: A solid bounded by six rectangular plane faces it called a cuboid. A cuboid has 6 rectangular faces, 12 edges and 8 vertices.

In the adjoining figure, $ABCDEFGH$ is a cuboid whose

1. Six  faces are: $ABCD, EFGH, EFBA, HGCD, EHDA\ and\ BFGC$.
2. Out of these, the four side faces, namely $EFBA, HGCD, EHDA, \ and\ BFGC$ are called lateral faces.
3. 12 edges are:$AB, CD, EF, GH, AE, DH, BF, CG, AD, EH, FG, and BC$.
4. Eight Vertices are: $A, B, C, D, E, F, G, and H$.

Cube: A cuboid whose length, breadth and height are all equal is called a cube. Each edge of a cube is called its side.

Formula for Cuboid and Cube

Consider a cuboid with $length=l, \ width=w \ and \ height=h$.

$Volume\ of\ a\ cuboid=(l\times b\times h) cubic\ units.$

$Total\ surface\ Area\ of\ a\ cuboid=2(lb+bh+lh) \ units.$

$Lateral \ surface \ Area \ of \ a \ cuboid = 2(l + b) \times h sq. units.$

$Diagonal\ of\ a\ cuboid=\sqrt{l^2+b^2+h^2} \ units$

Consider a cube with all sides equal to $a$ units.

$Volume \ of \ a \ cube = a^3 \ cubic \ units.$

$Total \ surface \ Area \ of \ a \ cube = 6a^2 \ units$

$Lateral \ surface\ Area\ of\ a\ cube=4a^2 \ units.$

$Diagonal \ of \ a \ cube = a\sqrt{3}$

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