Points to Remember- Visualising Solid Shapes | Class 8 Mathematics by VP Classes PDF Download

Points to Remember 
• Perspective is the art of representing solid objects on a flat surface to show its height, width, distance, etc.
• 3-D bodies have different views from different positions.
• For a polyhedron,
F + V – E = 2
where ‘F’ stands for number of faces,
‘V’ stands for number of vertices and
‘E’ stands for number of edges.
• The relation F + V – E = 2 is called Euler’s formula.

WE KNOW THAT
Plane shapes have two dimensions (measurements) like length and breadth. That is why they are called two dimensional (2-D) shapes. On the other hand, a solid object having three dimensions like length, breadth, height (or depth) is called 3-D object. Triangles, rectangles, circles, trapeziums, etc. are 2-D Figures while cuboids, cubes, cylinders, spheres, etc. are 3-D objects.
A solid is bounded by one or more surface and it always occupies some space. Its surface (or face) can be a plane or a curved surface. When any two faces of a solid meet together, we get a line segment called an edge. When three more faces of a solid meet at one point, then the point is called a vertex of the solid.

Note: 
Perspective is an art of representing solid objects on f lat surfaces to convey the impression of distance, depth, width and height, using oblique lines and shading.

Solved Example
Q1: Which of the following is true for a polyhedron?
1. Polyhedrons are 3D figures.
2. They always have a closed surface.
3. A line joining any two points on the surface always lies in inside the shape.
4. Both bases are parallel to each other.
Solution: (1) and (2) are true.

Q2. Draw a street route from the library to bus depot.
Solution: The shortest route from the library to bus depot is –

Move from the library towards the north and take a right turn from the locality and go straight passing from the primary school, fire station and City Park. In the front of the lake is our bus depot.

Q3. Which is further east, the city park or the market?
Solution: Between the market and the city park, the city park is further east.

Q4. Which is further south, the primary school or senior secondary school?
Solution: Between the primary school and the senior secondary school, the senior secondary school is further south. Thus we observe that the effective use of colours has made easy to find the respective locations and we can also find the path where we need to travel.