Class 8 RD Sharma Solutions - Chapter 19 Visualising Shapes - Exercise 19.2

Understanding shapes and their properties is fundamental in geometry. Class 8 RD Sharma’s Chapter 19 focuses on visualizing shapes helping students grasp spatial relationships and geometric concepts. Exercise 19.2 specifically deals with the problems that enhance the ability to visualize and manipulate different shapes contributing to a deeper understanding of the geometric figures.

Visualizing Shapes

Visualizing shapes involves mentally manipulating and understanding geometric figures in various positions and orientations. This skill is crucial for solving complex geometric problems and proofs. In Exercise 19.2 students work on the problems that require them to visualize transformations such as the rotation, reflection, and translation applied to the various shapes. The exercise helps in developing spatial awareness and problem-solving skills by engaging students in activities that involve constructing and deconstructing geometric figures.

Question 1. Which of the following are nets for a cube?

Solution:

Diagram (iv), (v), (vi) are the nets for a cube.

Question 2. Name the polyhedron that can be made by folding each net:

Solution:

(i) By folding each net a square pyramid can be formed.

(ii) By folding each net a triangular prism can be formed.

(iii) By folding each net a triangular prism can be formed.

(iv) By folding each net a hexagonal prism can be formed.

(v) By folding each net a hexagonal prism can be formed.

(vi) By folding each net a Cuboid can be formed.

Question 3. Dice are cubes where the numbers on the opposite faces must total 7. Which of the following are dice?

Solution:

The Figure (i) form a dice and the total sum of numbers on opposite faces is 7.

Question 4. Draw nets for each of the following polyhedrons:

Solution:

(i) Below image shows the net pattern for cube.

(ii) Below image shows the pattern for triangular prism.

(iii) Below image shows the net pattern for hexagonal prism.

(iv) Below image shows the net pattern for pentagonal pyramid.

Question 5. Match the following figures:

Solution:

(a) ⇒ (iv) 

Here, the multiplication of numbers on adjacent faces are equal, i.e., 6×4 = 24 and 4×4 = 16

(b) ⇒ (i) 

Here, the multiplication of numbers on adjacent faces are equal, i.e., 3×3 = 9 and 8×3 = 24

(c) ⇒ (ii) 

Here, the multiplication of numbers on adjacent faces are equal, i.e., 6×4 = 24 and 6×3 = 18

(d) ⇒ (iii) 

Here, the multiplication of numbers on adjacent faces are equal, i.e., 3×3 = 9 and 3×9 = 7

Conclusion

Exercise 19.2 in Chapter 19 of RD Sharma’s textbook is essential for the enhancing spatial visualization skills. By practicing these problems students build a solid foundation in the geometric concepts that are vital for the higher mathematics. The exercise not only aids in understanding the shapes but also prepares students for the more advanced topics in the geometry and other mathematical areas.