RBSE Solutions Class 8 Maths Chapter 8 Visualization of Solids Exercise 8.1

Question 1. Fill in the blanks
(i) The base of pyramid is a polygon and other faces have the____shape. (triangle/parallelogram)
(ii) Base face and top face of a prism are ____ of each other. (congruent/similar)
(iii) A polyhedron whose vertices are 10 and faces are 7 then its edges are ____ (15/19)
(iv) Cube and cuboid are also a kind of ____ (prism/pyramid)
Answer:
(i) The base of a pyramid is a polygon, and its other faces are always triangular in shape. A pyramid has triangular faces that meet at a single point.
(ii) The base face and top face of a prism are congruent to each other, meaning they are identical in shape and size. They are parallel and look exactly the same.
(iii) For a polyhedron, if the number of vertices is 10 and the number of faces is 7, then its edges are 15. This follows Euler's formula for polyhedra, which connects faces, vertices, and edges.
(iv) A cube and a cuboid are both special types of prisms. They have two identical and parallel bases, and rectangular side faces.
In simple words: Pyramids have triangular sides. Prisms have identical top and bottom faces. You can find the number of edges for a polyhedron using a special formula. Cubes and cuboids are types of prisms.

🎯 Exam Tip: Remember Euler's formula for polyhedra: \( V - E + F = 2 \), where V is vertices, E is edges, and F is faces. This formula helps relate the different parts of any polyhedron.

Question 2. Write any four solid polyhedrons surrounding you with number of its vertices, faces and edges.
Answer: Many everyday objects are polyhedrons. Here are four examples from around us, showing their faces, edges, and vertices:

🎯 Exam Tip: When listing polyhedrons, always try to pick common items that clearly fit the definition and state their exact number of faces, edges, and vertices.

Question 4. Recognize polyhedron shapes in the following organized shapes also tell that which shapes are used to organized these shapes.
Answer: The figures provided show combinations of polyhedral shapes. Identifying their individual components helps understand complex structures.
Figure (i) and (ii) represent polyhedrons, which are three-dimensional shapes made of flat polygonal faces, straight edges, and sharp corners or vertices.
Figure (i) is created by combining a cuboid and a pyramid. The cuboid forms the base, and a pyramid sits on top of it.
Figure (ii) is made by combining a prism and a pyramid. The prism acts as the main body, and a pyramid is placed on its top surface.
In simple words: The first two pictures show solids made by joining basic shapes. Picture (i) is a box (cuboid) with a pointy shape (pyramid) on it. Picture (ii) is a prism with a pyramid on top.

🎯 Exam Tip: When asked to identify combined shapes, break down the complex figure into simpler, recognizable geometric solids like cuboids, prisms, and pyramids. Clearly state each component shape.