Three-Dimensional Figures
Three-dimensional figures are discussed here with the figures or pictures along with the explanation.
Solids: Objects having fixed shape and size, and occupying fixed space are called solids.
Solids occur in various geometrical shapes. These shapes are known three-dimensional figures.
Some 3-D shapes are namely cuboids, cubes, cylinders and cones.
We will discuss about some of the 3-dimensional figures having flat faces, namely cubes, cuboids, prisms, pyramids and tetrahedrons.
Faces, Vertices and Edges of a 3-dimensional Figure:
(i) Faces: Each flat part of a solid is called its face.(ii) Vertices: Each corner where three faces of a solid meet is called its vertex. The plural of vertex is vertices.
(iii) Edges: The two faces of a solid meet in a line, called an edge.
Now, we shall discuss about the faces, vertices and edges of some 3-dimensional figures having flat faces.
| Name of Solid | Number of Faces | Number of Vertices | Number of Edges |
|---|---|---|---|
| Cuboid | 6 | 8 | 12 |
| Cube | 6 | 8 | 12 |
| Triangular Prism | 2 triangular, 3 rectangular | 6 | 9 |
| Square Pyramid | 1 square face, 4 triangular faces | 5 | 8 |
| Rectangular Pyramid | 1 rectangular face, 4 triangular faces | 5 | 8 |
| Triangular Pyramid (or Tetrahedron) | 4 triangular faces | 4 | 6 |
I. Cuboid:
A solid bounded by six rectangular plane faces is called a cuboid.A box, a matchbox, a book, a brick, a tile, etc., are all in the shape of a cuboid.
In the adjoining figure, ABCDEFGH is a cuboid.
(i) Faces of a Cuboid:
A cuboid has 6 faces.
In the given figure, the 6 faces of the cuboid are:
ABCD, EFGH, ADHE, BCGF, ABFE and DCGH.
(ii) Vertices of a Cuboid:
A cuboid has 8 vertices.
In the given figure, the 8 vertices of the cuboid are:
A, B, C, D, E, F, G, H.
(iii) Edges of a Cuboid:
A cuboid has 12 edges.
In the given figure, the 12 edges of the cuboid are:
AB, BC, CD, DA, EF, FG, GH, HE, AE, DH, BF, CG.
II. Cube:
A cuboid whose length, breadth and height are equal is called a cube.
Dice, sugar cubes, ice cubes, etc., are all examples of a cube.
In the adjoining figure, ABCDEFGH is a cube.
(i) Faces of a Cube:
A cube has 6 faces.
In the given figure, the 6 faces of the cube are:
ABCD, EFGH, ADHE, BCGF, ABFE and DCGH.
(ii) Vertices of a Cube:
A cube has 8 vertices.
In the given figure, the 8 vertices of the cube are:
A, B, C, D, E, F, G, H.
(iii) Edges of a Cube:
A cube has 12 edges.
In the given figure, the 12 edges of the cube are:
AB, BC, CD, DA, EF, FG, GH, HE, AE, DH, BF, CG.
Note:
Here, in three-dimensional figures we will discuss about right prism arid regular pyramid.
III. PRISM:
A solid whose two faces are parallel plane polygons and the side faces are rectangles is called a prism.Triangular Prism:
A triangular prism is made up of two parallel end-faces each one of which is a triangle and three lateral faces each one of which is a rectangle.
In the adjoining figure, ABCDEF is a triangular prism.
(i) Faces of a Triangular Prism:
A triangular prism has 2 triangular faces and 3 rectangular faces.
In the given figure,
2 triangular faces are ∆ABC and ∆DEF,
3 rectangular faces are ABED, ADFC and CBEF.
(ii) Vertices of a Triangular Prism:
A triangular prism has 6 vertices.
In the given figure, the 6 vertices of the triangular prism are A, B, C, D, E, F.
(iii) Edges of a Triangular Prism:
A triangular prism has 9 edges.
In the given figure, the 9 edges of the triangular prism are:
AB, BC, CA, DE, EF, FD, AD, BE, CF
Note:
A cuboid is also called a rectangular prism.
IV. PYRAMID:
A pyramid is a solid whose base is a plane rectilinear figure whose side faces are triangles having a common vertex, called the vertex of the pyramid.(a) Square Pyramid:
It is a solid whose base is a square and whose side faces are triangles having a common vertex.
In the adjoining figure, OABCD is a square pyramid with its vertex at O.
(i) Vertices of a Square Pyramid:
A square pyramid has 5 vertices.
In the given figure, OABCD is a square pyramid having O, A, B, C, D as its vertices.
(ii) Faces of a Square Pyramid:
A square pyramid has faces one of which is a square face and the rest four are triangular faces.
In the given figure, OABCD is a square pyramid having ABCD as its square face and OAD, OCD, OBC and OAB as its triangular faces.
(iii) Edges of a Square Pyramid:
A square pyramid has 8 edges.
In the given figure, the square pyramid OABCD has 8 edges, namely, AB, BC, CD, DA, OA, OB, OC and OD.
(b) Rectangular Pyramid:
It is a solid whose base is a rectangle and whose side faces are triangles having a common vertex.
In the adjoining figure, OABCD is a rectangular pyramid.
(i) It has 5 vertices, namely O, A, B, C, D.
(ii) It has 1 rectangular face, namely ABCD, and 4 triangular faces, namely OAD, ODC, OAB, OBC
(iii) It has 8 edges, namely AB, BC, CD, DA, OA, OB, DC, OD
(c) Triangular Pyramid (Tetrahedron):
It is a solid whose base is a triangle and whose side faces are triangles having a common vertex.
In the adjoining figure, OABC is a triangular pyramid.
(i) It has 4 vertices, namely O, A, B, C.
(ii) It has 4 triangular faces, namely ABC, OAB, OAC and OBC.
(iii) It has 6 edges, namely OA, OB, OC, AB, AC, BC.
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