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Exploring Some Geometric Terms Exercise 4.6 Class 8 Maths – Chapter 4 NCERT Solutions
NCERT Class 8 Maths Chapter 4 Geometric Terms Exercise 4.6 detailed solutions, along with important concepts, are provided by the ALLEN faculty team on this webpage for better understanding and practice. The detailed solutions are prepared in a way that makes learning easier and more effective for students.Exercise 4.6 involves joining four cubes in different ways to make different arrangements; using an isometric grid to draw 3D objects; learning about 3D shapes by drawing isometric shapes; and looking at the Penrose staircase and the impossible triangle.
1.0Download Class 8 Maths Chapter 4 Ex 4.6 NCERT Solutions PDF
Download the detailed NCERT Class 8 Maths Exercise 4.6 Solutions PDF for better understanding and effective practice.
2.0Detailed NCERT Solutions on Geometric Terms Exercise 4.6 Class 8 Maths (Ganita Prakash Term 2)
1. In addition to the 5 ways shown in Fig, are there any additional ways of gluing four cubes together along faces? Can you visualise and draw these as well? (i)
Sol.
Hint: Consider a protion of this figure that is physically realisable and identify the 3 primary directions.
Sol. The picture shows the Penrose staircase. It is a special type of optical illusion. It looks like a staircase that keeps going down (or up) forever in a loop. But in reality, such a staircase cannot exist.
In the illusion:
Every step looks like it is going downward.
If a ball is placed on the stairs, it appears to roll down.
The staircase forms a loop, so the ball comes back to the starting point.
This makes it look like the ball is rolling forever without stopping. So, it creates an illusion of endless motion.
In real life:
- This staircase cannot be made in real 3D space.
- If we try to build it:
- One part will have to go upward, or
- The loop will not close properly.
So, the ball will:
- Roll down to the lowest point
- Then stop or roll back
It cannot roll forever in reality.
- In the picture → ball rolls forever (illusion)
- In real life → ball stops at the lowest point
- Observe this triangle.
4. (i) Would it be possible to build a model out of actual cubes? What are the front, top and side profiles of this impossible triangles? (ii) Recreate this on an isometric grid. (iii) Why does the illusion work?
Sol. (i) The impossible triangle using cubes creates an optical illusion where three straight beams of square crosssection appear to form a continuous, closed loop.
It can be built using cubes of the same size in the following steps.
Step-1: Bottom Row: Lay a horizontal row of 4-5 cubes.
Step-2: Vertical Row: At one end, stack 4-5 cubes vertically to form a 90degree corner.
Step-3: The "Gap" Row: At the top of the vertical stack, extend a row of cubes horizontally away from the viewer (into the depth of the scene) When observed through a camera at a specific angle, the end of this third row will appear to "touch" the first horizontal row, even though they are feet apart. Front, side, and top views are as follows. (ii) Recreate this on an isometric grid.
It would look like this
(iii)Isometric Limitation:
In isometric drawing, there is no perspective.
- In real life, things that are far away look smaller.
- But in isometric drawings, objects stay the same size, even if they are far.
Because of this, your eyes can get confused.
It may look like something far away is actually right next to something in front.
3.0Key Concepts of Chapter 4 Geometric Terms Exercise 4.6
- Arranging four cubes to form different 3D structures
- Representing 3D objects using an isometric grid
- Visualising 3D objects through 2D drawings
- Understanding the Penrose staircase illusion
- Exploring the impossible triangle
- Limitations of isometric representations
4.0Benefits of NCERT Solutions Class 8 Maths Chapter 4 Exercise 4.6
- Represents 3D objects using an isometric grid.
- Explores different structures formed by arranging four cubes.
- Interprets 3D shapes through 2D isometric drawings.
- Examines the Penrose staircase as a geometric visual illusion.
- Understands the impossible triangle.
- Identifies the limitations of representing 3D objects through 2D drawings.