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Exploring Some Geometric Terms Exercise 4.5 Class 8 Maths – Chapter 4 NCERT Solutions
NCERT Class 8 Maths Chapter 4 Exercise 4.5 detailed solutions provided by the experienced ALLEN mentors are given below, along with important concepts and benefits. These solutions can be useful for Class 8 students in their academic studies and for competitive exams such as Olympiads.Exercise 4.5 focuses on projections of identical cube arrangements, their top, front and side views, constructing solids from given projections, counting cubes in layers, and the different shapes formed by a cube under various orientations.
1.0Download Class 8 Maths Chapter 4 Ex 4.5 NCERT Solutions PDF
Download the detailed solution PDF at your convenience and practise the questions along with the solutions.
2.0Detailed NCERT Solutions on Geometric Terms Exercise 4.5 Class 8 Maths (Ganita Prakash Term 2)
Figure it out-05
1. Draw the top view, front view and the side view of each of the following combination of identical cubes.
| Front view | Side View | Top View | |
| (a) | | □ | |
| (b) | | | |
| (c) | □ | □ | |
| (d) | | | |
| (e) | | | |
Right Side View (i)
(iii)
Front View Top View Side View
(vii)
Top view
Top view
Front view
Sol: Solid (ii) Now,
- Since front view has a small gap on top right side, (i), (v) and (vii) cannot be possible
- In top view, there is a gap on the right corner- which means in solid front right side should be a gap at the corner- So, (iii) and (vi) are not possible.
- From (ii) and (iv)- we can draw them and see.
This matches our the views in the question Thus, the correct answer is solid (ii). (i)
(iii)
- Using identical cubes, make a solid that gives the following projections.
(ii)
Front view (iv)
(v)
(vii)
(vi)
Side view (viii)
(ix)
Sol. (i)
Sol. This is a tetrahedral pyramid. We count layer by layer from the top: 1 (top) +3 (second layer) +6 (third layer) +10 (bottom layer) = 20 cubes in total. Counting from the top layer to the bottom layer: cubes
6. What are the different shapes the projection of a cube can make under different orientations?
Sol: Five different shapes can be observed. (a) Square Orientation: One face of the cube is parallel to the projection plane. (b) Rectangle Orientation: Two faces are visible, but one set of edges is parallel to the plane. (c) Parallelogram Orientation: A face is tilted relative to the plane. (d) Rhombus Orientation: A special tilted case where all projected edges remain equal. (e) Hexagon (maximum case) Orientation: The cube is oriented so that three faces are equally visible (e.g., looking along a body diagonal)
3.0Key Concepts of Chapter 4 Geometric Terms Exercise 4.5
- Top, front and side views of cube arrangements
- Projections of combinations of identical cubes
- Constructing 3D solids from given projections
- Counting cubes in different layers of a solid
- Tetrahedral pyramid made using identical cubes
- Different projections of a cube based on its orientation
- Shapes formed by cube projections, including square, rectangle, parallelogram, rhombus and hexagon
4.0Benefits of NCERT Solutions Class 8 Maths Chapter 4 Exercise 4.5
- Identifies the top, front and side views of identical cube arrangements.
- Interprets 2D projections of 3D cube structures.
- Forms cube arrangements corresponding to given projections.
- Determines the number of cubes in different layers of a solid.
- Represents a tetrahedral pyramid using identical cubes.
- Examines cube projections under different orientations.
- Distinguishes square, rectangle, parallelogram, rhombus and hexagon projections of a cube.