## Geometry Chapter 1 Geometrical Concept Regarding The Formation Of Regular Solid Bodies

**Geometry Chapter 1 Introduction:**

- In our daily life, we encounter and also get in contact directly with different types of bodies within and outside our houses.
- For example chair, table, book, pen, pencil, brick, die, ball, plate, glass, candle, electric bulb, box, pipe, drum, etc.
- These are called
**solid bodies.** - Some of them have length, breadth, and thickness; some of them have length and breadth but no thickness.
- We also observe that among all the objects around us, there are some which have consistency in shapes and others that do not have consistency in shapes.
- We take a straight line. We find that it has only length, it has no breadth and height. Again we take a brick.
- It has all three lengths, breadth, and height.
- A ludo die has consistency in shape but a piece of broken glass has no consistency in shape.

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## Geometry Chapter 1 Regular and Irregular figures or objects

**Regular objects:**

- The objects which have consistency in shape are called Regular objects.
- If we place a string over the object and when it is stretched along the body of the object, the string is symmetrical with the body then the object is regular.

**For example:**

- Books,
- Football,
- The wall of a building,
- Bricks,
- Boxes,
- Pencils,
- Scales,
- Drums,
- Benches,
- Chairs,
- Tables,
- Plates,
- Glass, etc. are regular objects.

**Irregular objects:**

- The objects which do not have consistency in shape are called Irregular objects.
- In the case of an irregular object, a stretched string when placed along its body of it is not symmetrical along the body of the object.
- Examples of irregular objects are A piece of broken glass, a piece of tattered paper, a broken wall, coal, etc.

**Regular Objects:**

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**Irregular Objects**

## Geometry Chapter 1 Solids

- The common property of each of the objects is that each space in the atmosphere has some weight.
- Let us consider a wooden box. It has some weight. Also, it has length, breadth, and height.
- If we consider the upper face of a table that has only length and breadth. It has no thickness or height.
- A single hair has only length.
: The length, breadth, and thickness of a body are called the**Dimensions**of the body.**Dimensions**- In the above examples, a wooden box has three dimensions Length, breadth, and height or thickness.
- The upper face of a table is two-dimensional in length and breadth.

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- A hair is a unidimensional length. The shadow of a building has two dimensions
- An object or a body having three dimensions length, breadth, and height, which occupies some space and has some weight is called a Solid.
: Chair, table, drum almirah, cube, book, brick, a ludo die, football, sphere cone, prism, pyramid, tetrahedron, etc.**Examples of solids**

## Geometry Chapter 1 Different Types Of Solids

Solids are of different shapes.

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** Solids of different shapes are discussed below:**

**Rectangular Parallelopiped :**

- A rectangular parallelopiped is a solid bounded by three pairs of parallel surfaces. It has 6 surfaces, 8 vertices, and 12 edges.
- The dimension of a rectangular parallelopiped is 3 and its two adjacent surfaces are at right angles to each other.
- Bricks, books, boxes, etc. are examples of rectangular parallelopiped.

**Cube :**

- If all the surfaces of a parallelopiped are squares,’ then the parallelopiped is called a
**Cube.** - It has six surfaces, eight vertices, and twelve edges.
- A ludo die is an example of a cube
- parallel and congruent. Each of them has five sides.
- The is a prism, its five side faces are parallelograms.
- The congruent end faces may be triangle, quadrilateral, or any polygon and their names are given accordingly as a triangular prism, quadrilateral prism, polygon prism, etc.
- The straight line obtained by the intersection of any two side faces is called a side edge.
- If the side edges are perpendicular to the end faces, then the prism is called a
**Right Prism.** **Oblique Prism.**

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**Pyramid**

- A solid body bounded by some plane faces is such that its base face is a polygon and the side faces are triangles having a common vertex is called a
**Pyramid.** - The common vertex of a pyramid is a point in space that lies outside the base face.
- The base face of a pyramid may be a triangle, quadrilateral, or polygon, and the side faces are some triangles having a common vertex.
- The adjoining figure is a pyramid. Its base face is a polygon of six sides (called hexagons) ABCDEF; it is called the base of the pyramid.
- P is the common vertex of the side faces which are six triangles. P is the vertex of the pyramid.
- The perpendicular drawn from the vertex, P upon the base is called the height of the pyramid.
- In the figure, PO is the height. The intersecting straight line by any two triangles in the side faces is called the side edge.
- If the perpendicular drawn from the vertex of a pyramid upon the base passes through the center of the base, the pyramid is called a
**Right Pyramid** - If the base of a right pyramid is a rectangle or a Square, then the perpendicular from the vertex upon the base passes through the point of intersection of the diagonals of the base.
- If the base of a right pyramid is a regular polygon i.e., the sides of the base are of equal length, the right pyramid is called
**a Regular Right Pyramid.** - The side faces of a right pyramid are congruent isosceles triangles.
- A pyramid is. not a right pyramid is called a
**Transverse Pyramid**The perpendicular drawn from the vertex of a pyramid upon any side of the base is called the**slant height.** - In PK is the slant height of the pyramid.

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Tetrahedron:

- If the base of a pyramid is a triangle, then it is called a
**Tetrahedron.** - A tetrahedron has four vertices, four plane faces, and six side edges.
- If the base of the tetrahedron is an equilateral triangle then it is called a
**Right Tetrahedron.** - If the four faces of a tetrahedron are equal equilateral triangles, then it is called a
**Regular Tetrahedron.**

Cone:

- The solid generated by the revolution
a right-angled triangle about one of the sides containing the right angle as an axis is called a**Of****Cone.** - ZAOP is the right angle of the right-angled triangle AOP.
- Revive the triangle about OP as an axis, then point A forms a circle.
- This circle is the base of the cone and OA is its radius, ZAPB is the vertical angle and P is the vertex of the cone.
- OP is perpendicular to the base and it is the height of the cone.
- AP is the slant height.
- The foremost part of the plantain flower (Mocha of banana), the sharpened end of a pencil, conical tent, etc. are examples of cones.
- The dimension of a cone is three.

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**Sphere :**

- The solid generated by the revolution of a semi-circle about its diameter as an axis is called a
**Sphere.** - The radius of the semi-circle is the radius of the sphere.
- The dimension of the sphere is three.
- Football, cricket ball, marble, etc. are examples of spheres.AB is the diameter and OA = OB = radius of the sphere, the center of the sphere.

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Cylinder:

- The solid generated by the revolution of a rectangle about one of its sides as an axis is called a
**Cylinder.** - It is called a right circular cylinder. Its dimension is three.
- Tin caskets, drums, full pencils, water pipes, candles, etc. are examples of cylinders.
- Considering the side AB of the rectangle ABCD as the axis, revolving the rectangle about it, CD forms a curved surface.
- In one complete revolution, a right circular cylinder is generated.
- The CD is the generating line and AB is the axis of the cylinder.
- Two end faces of it are two parallel circles.
- AB is the height and AD is the radius of the base circle.