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”.
Area is measurement of space enclosed by a closed geometrical figure.
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.
Formation of Solid Solids
Stacking of 2 dimensional figures, results in solids shapes.
Example: Linear stacking of circles, forms the solid shape called cylinder.
Solids and Their Classification
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°.
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.
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
A cuboid is a solid bounded by six rectangular plane regions.
It is formed by stacking rectangles linearly.
Solid Triangular Prism
Solid Triangular Prism: A polyhedron with two triangular bases parallel to each other. It is formed by stacking triangles linearly.
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.
Solid cylinder can be formed in two different ways:
(i) By stacking rectangles in a circular fashion.
(ii) By stacking many circles linearly
Solid spheres are formed by stacking circles in a circular fashion.
Solid Cones are formed by stacking triangles which are right-angled, in a circular fashion with edge which is right angled at the center.
Formation of Hollow Solids
Hollow Solids are obtained by joining two dimensional figures.
Hollow Cuboid: Formed by joining six rectangles in a specific manner as shown below:
Hollow Triangular Prism
Hollow triangular prism: Formed by joining two triangles and three rectangles in a specific manner as shown below:
Hollow Hexagonal Prism
Hollow hexagonal Prism: Formed by joining two hexagons and six rectangles as shown below:
Hollow Hexagonal Prism
Hollow Cylinder: A cylinder is made by rotating a rectangle around either its length or breadth as shown below.
Hollow Cone: A circle and a curved sector of a circle are joined together as shown below:
Pyramid: All side faces are triangular in shape and base is of the shape of any polygon.
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.
(ii) Concave Polyhedron:
A polyhedron whose surface intersect itself.
Line segment joining any two points of the polyhedron may lie in the exterior part.
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.
Euler’s Formula: For any polyhedron,
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
Side, front and top view of the above solid (made up of cubes) is as shown below: