Visualising Solid Shapes Class 8 Notes: Chapter 10

Introduction

Visualising Solid Shapes Class 8 Notes provided here are the right tool for students to study productively and score better marks in the exams. Chapter 10 notes will help students get a complete overview of the chapter and also a clear insight into the important topics to remember. The CBSE notes further come with detailed information about each topic and students can have an effective revision before the exams.

Two Dimensional Object

A shape with only two dimensions (such as length and width) and no thickness is called two-dimensional shape. Squares, Circles, Triangles, etc are two dimensional objects. Also known as “2D”.

CBSE Class 8 Maths Notes Chapter 10 - 2

Area

Area is measurement of space enclosed by a closed geometrical figure.

Volume

Volume is measurement of total space occupied by a solid.

Three Dimensional Objects- Solids

Shapes which can be measured in 3 directions are called three-dimensional shapes. These shapes are also called solid shapes. Length, width, and height (or depth or thickness) are their dimensions.

CBSE Class 8 Maths Notes Chapter 10 - 1

Formation of Solid Solids

Stacking of 2 dimensional figures, results in solids shapes.
Example: Linear stacking of circles, forms the solid shape called cylinder.

CBSE Class 8 Maths Notes Chapter 10 - 2

Solids and Their Classification

Hexagon

In geometry, hexagon is a polygon with 6 sides. Sum of all interior angles is equal to 720°.
If all the sides of hexagon are equal then it is called regular hexagon, then each interior angle measures 120°.

CBSE Class 8 Maths Notes Chapter 10 - 3

CBSE Class 8 Maths Notes Chapter 10 - 4

Non-Polyhedrons

Solids with curved faces are called Non polyhedrons. They also can be discribed as solids which have sides that are not polygons.
Example: Sphere, Cylinder, Cone, etc.

CBSE Class 8 Maths Notes Chapter 10 - 5

Polyhedrons

A Polyhedron is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices. In short, Solids with flat surfaces are called Polyhedrons.(or Polyhedra)

Regular polyhedron: All faces constitute regular polygons and at each vertex the same number of faces intersect. Example : Cube

CBSE Class 8 Maths Notes Chapter 10 - 6

Solid Cuboid

A cuboid is a solid bounded by six rectangular plane regions.
It is formed by stacking rectangles linearly.

CBSE Class 8 Maths Notes Chapter 10 - 7

Solid Triangular Prism

Solid Triangular Prism: A polyhedron with two triangular  bases parallel to each other. It is formed by stacking triangles linearly.

CBSE Class 8 Maths Notes Chapter 10 - 8

Solid Hexagonal Prism

Solid Hexagonal Prism: A polyhedron with two hexagonal  bases parallel to each other. It is formed by stacking hexagons linearly. Each face of hexagonal prism is rectangular in shape.

                                        CBSE Class 8 Maths Notes Chapter 10 - 9

                                            Solid Hexagonal Prism

Solid Cylinder

Solid cylinder can be formed in two different ways:

(i) By stacking rectangles in a circular fashion.

(ii) By stacking many circles linearly

CBSE Class 8 Maths Notes Chapter 10 - 11

Solid Sphere

Solid spheres are formed by stacking circles in a circular fashion.

CBSE Class 8 Maths Notes Chapter 10 - 12

Solid Cone

Solid Cones are formed by stacking triangles which are right-angled, in a circular fashion with edge which is right angled at the center.

CBSE Class 8 Maths Notes Chapter 10 - 13

Formation of Hollow Solids

Hollow Solids are obtained by joining two dimensional figures.

Hollow Cuboid

Hollow Cuboid: Formed by joining six rectangles in a specific manner as shown below:

CBSE Class 8 Maths Notes Chapter 10 - 14

Hollow Triangular Prism

Hollow triangular prism: Formed by joining two triangles and three rectangles in a specific manner as shown below:

CBSE Class 8 Maths Notes Chapter 10 - 15

Hollow Hexagonal Prism

Hollow hexagonal Prism: Formed by joining two hexagons and six rectangles as shown below:

CBSE Class 8 Maths Notes Chapter 10 - 16

Hollow Hexagonal Prism

Hollow Cylinder

Hollow Cylinder: A cylinder is made by rotating a rectangle around either its length or breadth as shown below.

CBSE Class 8 Maths Notes Chapter 10 - 17

 

CBSE Class 8 Maths Notes Chapter 10 - 18

Hollow Cone

Hollow Cone: A circle and a curved sector of a circle are joined together as shown below:

CBSE Class 8 Maths Notes Chapter 10 - 19

Hollow Cone

Pyramid

Pyramid: All side faces are triangular in shape and base is of the shape of any polygon.

CBSE Class 8 Maths Notes Chapter 10 - 20

Types of Polyhedrons

Polyhedrons are of two types:

(i) Convex Polyhedron:
A polyhedron whose surface (comprising its faces, edges and vertices) does not intersect itself.
Line segment joining any two points of the polyhedron lies within its interior part or on surface.

CBSE Class 8 Maths Notes Chapter 10 - 21

(ii) Concave Polyhedron:
A polyhedron whose surface intersect itself.
Line segment joining any two points of the polyhedron may lie in the exterior part.

CBSE Class 8 Maths Notes Chapter 10 - 22

Faces, Edges and Vertices

Every individual flat surface of a solid is called its face. Solids have more than one face.
Example: Cube and cuboids have six faces.

Line segment which acts as an interface between two faces is called an edge. It is the line segment that joins two vertices.
Example: Cube and cuboids have 12 edges.

A vertex is a point where two or more edges meet. These are corner points.
Example: Cube and cuboids have 8 vertices.

CBSE Class 8 Maths Notes Chapter 10 - 23

Euler’s Formula

Euler’s Formula: For any polyhedron,

F+VE=2,

where ‘F’ stands for number of faces, V stands for number of vertices and E stands for number of edges.

Perspectives of 3D Shapes

Perspectives of Looking at a Solid

CBSE Class 8 Maths Notes Chapter 10 - 24
Side, front and top view of the above solid (made up of cubes) is as shown below:
CBSE Class 8 Maths Notes Chapter 10 - 25

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