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A solid has three dimensions, namely, length, breadth or width and height or thickness. The plane surfaces that binds it are called its faces and the solid so generated is known as a polyhedron.
The volume of any solid figure is the amount of space enclosed within its bounding faces. A solid has edges, vertices and faces which are shown in the figure given below:
Description: 16-1.tif

A solid has two types of surface areas:
  • Lateral Surface Area (LSA) LSA of a solid is the sum of the areas of all the surfaces it has except the top and the base.
  • Total Surface Area (TSA) TSA of a solid is the sum of the lateral surface area and the areas of the base and the top.
Note In case of solids like the cube and cuboid, the lateral surface area consists of plane surface areas (i.e., area of all surfaces except the top and base) whereas in case of solids like cone and cylinder, it consists of curved surface areas (CSA). Thus, for such solids the LSA is also called CSA.

Euler’s Rule

Euler’s rule states that for any regular solid:
Number of faces (F) + Number of vertices (V) = Number of Edges (E) + 2


A cuboid is a rectangular solid having 6 rectangular faces. The opposite faces of a cuboid are equal rectangles. A cuboid has a length (l), breadth (b) and height (h).
Description: 16-2.tif
In Fig. 2 ED is the diagonal of the cuboid. Moreover, the area of the surface GDCH is x, the area of the surface HEBC is y and the area of the surface GFEH is z.
  • Volume = Area of base × Height = lbh
  • Volume = Description: 2170.png
  • Volume = xh = yl = zb
  • Lateral surface area (LSA) or area of the 4 walls = 2 (l + b) h
  • Total surface area (TSA) = 2(x+y+z) = 2 (lb+bh + lh)
  • Diagonal = Description: 2179.png

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