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 SolidNumber of FacesNumber of VerticesNumber of Edges
Cuboid6812
Cube6812
Triangular Prism2 triangular, 3 rectangular69
Square Pyramid1 square face, 4 triangular faces58
Rectangular Pyramid1 rectangular face, 4 triangular faces58
Triangular Pyramid (or Tetrahedron)4 triangular faces46


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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