WBBSE Notes For Class 6 Maths Geometry Chapter 1 Geometrical Concept Regarding The Formation Of Regular Solid Bodies

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

Geometry Chapter 1 Introduction:

1. In our daily life, we encounter and also get in contact directly with different types of bodies within and outside our houses.
2. For example chair, table, book, pen, pencil, brick, die, ball, plate, glass, candle, electric bulb, box, pipe, drum, etc.
3. These are called solid bodies.
4. Some of them have length, breadth, and thickness; some of them have length and breadth but no thickness.
5. 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.
6. We take a straight line. We find that it has only length, it has no breadth and height. Again we take a brick.
7. It has all three lengths, breadth, and height.
8. 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:

1. The objects which have consistency in shape are called Regular objects.
2. 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:

1. Books,
2. Football,
3. The wall of a building,
4. Bricks,
5. Boxes,
6. Pencils,
7. Scales,
8. Drums,
9. Benches,
10. Chairs,
11. Tables,
12. Plates,
13. Glass, etc. are regular objects.

Irregular objects:

1. The objects which do not have consistency in shape are called Irregular objects.
2. 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.
3. 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

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

Simplification Maths Class 6

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

 

 

Geometry Chapter 1 Different Types Of Solids

Solids are of different shapes.

Class 6 Math Solution WBBSE

Solids of different shapes are discussed below:

 

Rectangular Parallelopiped :

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

 

 

Cube :

1. If all the surfaces of a parallelopiped are squares,’ then the parallelopiped is called a Cube.
2. The length, breadth, and height of a cube are equal. It is a three-dimensional solid body.
3. It has six surfaces, eight vertices, and twelve edges.
4. A ludo die is an example of a cube
5. parallel and congruent. Each of them has five sides.
6. The is a prism, its five side faces are parallelograms.
7. 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.
8. The straight line obtained by the intersection of any two side faces is called a side edge.
9. If the side edges are perpendicular to the end faces, then the prism is called a Right Prism.
10. If the side edges are not perpendicular to the end faces, then the prism is called Oblique Prism.

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Pyramid

1. 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.
2. The common vertex of a pyramid is a point in space that lies outside the base face.
3. The base face of a pyramid may be a triangle, quadrilateral, or polygon, and the side faces are some triangles having a common vertex.
4. 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.
5. P is the common vertex of the side faces which are six triangles. P is the vertex of the pyramid.
6. The perpendicular drawn from the vertex, P upon the base is called the height of the pyramid.
7. In the figure, PO is the height. The intersecting straight line by any two triangles in the side faces is called the side edge.
8. 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
9. 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.
10. 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.
11. The side faces of a right pyramid are congruent isosceles triangles.
12. 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.
13. In PK is the slant height of the pyramid.

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Tetrahedron:

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

Cone:

1. The solid generated by the revolution Of a right-angled triangle about one of the sides containing the right angle as an axis is called a Cone.
2. It is also called a right circular cone.
3. ZAOP is the right angle of the right-angled triangle AOP.
4. Revive the triangle about OP as an axis, then point A forms a circle.
5. 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.
6. OP is perpendicular to the base and it is the height of the cone.
7. AP is the slant height.
8. The foremost part of the plantain flower (Mocha of banana), the sharpened end of a pencil, conical tent, etc. are examples of cones.
9. The dimension of a cone is three.

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Sphere :

1. The solid generated by the revolution of a semi-circle about its diameter as an axis is called a Sphere.
2. It is bounded by a surface.
3. The radius of the semi-circle is the radius of the sphere.
4. The dimension of the sphere is three.
5. 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.

 

Simplification Questions For Class 6

Cylinder:

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