RBSE Solutions Class 8 Maths Chapter 8 Visualization of Solids Important Questions

I. Objective Type Questions

 

Question 1. Plane figures are called
(a) multi-dimensional
(b) three-dimensional
(c) two-dimensional
(d) none of the options
Answer: (c) two-dimensional
In simple words: Flat shapes like squares or circles are called two-dimensional because they only have length and width. They don't have any thickness.

🎯 Exam Tip: Remember that "dimension" refers to a measurement like length, width, or height. Plane figures only have two of these.

 

Question 2. Number of vertices in a cuboid are
(a) 12
(b) 8
(c) 6
(d) 4
Answer: (b) 8
In simple words: A cuboid is like a brick or a shoebox. The points where its edges meet are called vertices, and there are exactly eight of them. Think of the corners of the box.

🎯 Exam Tip: Visualizing common 3D shapes like cuboids helps in quickly recalling their properties such as vertices, faces, and edges.

 

Question 3. Every solid shape is made up of various two dimensional figures. These are called
(a) edges
(b) vertices
(c) faces
(d) cuboid
Answer: (c) faces
In simple words: When you look at a 3D object like a cube, its flat sides are 2D shapes, and these flat sides are known as its faces. For example, a cube has square faces.

🎯 Exam Tip: Understand the basic parts of a solid shape: faces (flat surfaces), edges (lines where faces meet), and vertices (points where edges meet).

 

Question 4. Euler's formula is
(a) \( F + V = E + 2 \)
(b) \( F - V = E-2 \)
Answer: (a) \( F + V = E + 2 \)
In simple words: Euler's formula helps us understand the relationship between the number of faces (F), vertices (V), and edges (E) of any simple 3D shape, like a cube or a pyramid. This formula is always true for polyhedrons.

🎯 Exam Tip: Memorize Euler's formula for polyhedrons, as it is a fundamental concept in the visualization of solids and is often tested.

 

Question 6. An example of three dimensional figure is
(a) cuboid
(b) circle
(c) square
(d) rectangle
Answer: (a) cuboid
In simple words: A cuboid has length, width, and height, making it a 3D shape. A circle, square, and rectangle are all flat 2D shapes.

🎯 Exam Tip: Differentiate between 2D and 3D figures by considering if they have depth or thickness in addition to length and width.

 

Question 7. Number of faces in a cuboid are
(a) 6
(b) 8
(c) 12
(d) 10
Answer: (a) 6
In simple words: A cuboid, like a box, has six flat surfaces. Imagine the top, bottom, front, back, and two side faces. These are its six faces.

🎯 Exam Tip: Always count the faces of a cuboid by visualizing its six sides: top, bottom, front, back, left, and right.

 

Question 8. Number of edges in a cube are
(a) 8
(b) 12
(c) 6
(d) 14
Answer: (b) 12
In simple words: A cube, which is a special type of cuboid where all faces are squares, has twelve edges. These are the lines where the faces meet.

🎯 Exam Tip: For a cube or cuboid, count the edges on the top face (4), bottom face (4), and the vertical connecting edges (4) to get a total of 12.

 

Question 9. Number of faces in a cube
(a) 12
(b) 8
(c) 6
(d) 10
Answer: (c) 6
In simple words: Just like a cuboid, a cube also has six flat faces. All these faces are square-shaped.

🎯 Exam Tip: Both cubes and cuboids have 6 faces, 8 vertices, and 12 edges. It's important to remember these common properties.

II. Fill in the Blanks

 

Question 1. Cuboid is a___shape.
Answer: three-dimensional
In simple words: A cuboid takes up space and has depth, so it is a three-dimensional shape.

🎯 Exam Tip: Recognize that 3D shapes occupy volume and can be viewed from different angles.

 

Question 2. 3D objects will have___views from different angles.
Answer: different
In simple words: When you look at a 3D object from different directions, it will appear to be shaped differently each time. For example, a house looks different from the front, side, or top.

🎯 Exam Tip: Practice drawing top, front, and side views of simple 3D objects to understand different perspectives.

 

Question 3. For any polyhedron, F + V =___is true.
Answer: \( E + 2 \)
In simple words: This is Euler's formula, which shows that if you add the number of faces and vertices of any polyhedron, the result is always equal to the number of edges plus two. This formula is a basic rule for solid shapes.

🎯 Exam Tip: Confirm Euler's formula with various polyhedrons like cubes or pyramids to ensure you remember it correctly.

 

Question 4. There is no reference or perspective in a___.
Answer: map
In simple words: A map shows locations from directly above, without any slanting view or sense of depth. It gives a bird's-eye view, so there's no perspective.

🎯 Exam Tip: Understand that maps provide a two-dimensional representation of an area, lacking the depth and angled view found in perspective drawings.

 

Question 5. ___is very important for drawing a picture but it is not relevant for a map.
Answer: Perspective
In simple words: Perspective is how things look smaller or bigger depending on how far away they are, which makes drawings look realistic. Maps, however, don't use perspective because they show everything from above, at a constant scale.

🎯 Exam Tip: Distinguish between a drawing that uses perspective to create an illusion of depth and a map that provides a flat, scaled representation.

 

Question. Write number of edges and faces in a triangular prism.
Answer: A triangular prism has 9 edges and 5 faces. It is a polyhedron with two parallel triangular bases and three rectangular sides.
In simple words: For a triangular prism, you will find 9 lines where the sides meet, and 5 flat surfaces in total.

🎯 Exam Tip: When counting faces and edges of a prism, remember its two identical bases and the rectangular faces connecting them.

 

Question 2. What are two dimensional shapes?
Answer: Two-dimensional shapes are flat figures that only have two measurements: length and breadth (or width). They do not have any thickness or depth. Common examples include squares and circles.
In simple words: 2D shapes are flat, like a drawing on paper. They only have length and width, not thickness.

🎯 Exam Tip: Focus on the two measurements (length and breadth) as the key characteristic defining two-dimensional shapes.

 

Question 3. Give 3 examples of two dimensional shapes.
Answer: Three examples of two-dimensional shapes are a triangle, a rectangle, and a circle. These shapes can be drawn on a flat surface and have no depth.
In simple words: Triangle, rectangle, and circle are all flat shapes, so they are 2D examples.

🎯 Exam Tip: Be ready to name common examples of both 2D and 3D shapes when asked.

 

Question 4. Give 3 examples of three dimensional shapes.
Answer: Three examples of three-dimensional shapes are a cuboid, a sphere, and a cylinder. These shapes take up space and have length, width, and height.
In simple words: Cuboid, sphere, and cylinder are shapes that have length, width, and height.

🎯 Exam Tip: Remember that 3D shapes are solid figures that you can hold, unlike flat 2D shapes.

 

Question 5. What is the definition of Prism?
Answer: A prism is a type of polyhedron where its base and top are identical and parallel polygons. All its other faces, called lateral faces, are parallelograms in shape. Prisms are common geometric shapes found in everyday objects.
In simple words: A prism is a 3D shape with two identical polygon ends that are parallel, and its sides are rectangles or parallelograms.

🎯 Exam Tip: The key features of a prism are its congruent and parallel bases and its parallelogram-shaped lateral faces.

 

Question 6. What do you mean by pyramid?
Answer: A pyramid is a polyhedron that has a polygonal base. Its sides are all triangular and they meet at a single point, which is called the common vertex or apex. The most famous pyramids are in Egypt.
In simple words: A pyramid is a 3D shape with a polygon base and triangle sides that all meet at a point at the top.

🎯 Exam Tip: Remember that all the lateral faces of a pyramid are triangles that converge at a single apex.

 

Question 8. Define a regular polyhedrons.
Answer: A polyhedron is called "regular" if all of its faces are made up of identical regular polygons. Also, the same number of faces must meet at every single vertex. The cube is a good example of a regular polyhedron.
In simple words: A regular polyhedron is a 3D shape where all its flat surfaces are the same regular polygon, and the same number of surfaces meet at every corner.

🎯 Exam Tip: To be "regular," a polyhedron needs both regular polygon faces and an identical arrangement of faces around each vertex.

 

Question 9. Is it possible to have a polyhedron with any given number of faces?
Answer: Yes, it is possible to have a polyhedron with different numbers of faces, but only if the number of faces is at least four. A polyhedron needs a minimum of four faces to enclose a 3D space.
In simple words: You can have a polyhedron with many faces, but it must have at least four faces.

🎯 Exam Tip: The minimum number of faces a polyhedron can have is four (e.g., a tetrahedron).

 

Question 10. Is a square prism same as a cube? Explain.
Answer: A square prism is not always the same as a cube. It can be a cube if all its faces are squares. However, a square prism can also be a cuboid, where its square bases are connected by rectangular faces that are not necessarily squares. A cube is a special type of square prism where all dimensions are equal.
In simple words: A square prism can be a cube if all its sides are equal squares. But it can also be a cuboid if its sides are rectangles, even if its top and bottom are squares.

🎯 Exam Tip: Remember that a cube is a specific type of square prism, but not all square prisms are cubes; some are cuboids.

 

Question 11. Can a polyhedron have 10 faces, 20 edges and 15 vertices?
Answer: We use Euler's formula to check this: \( F + V = E + 2 \).
If we substitute the given values:
\( 10 + 15 = 20 + 2 \)
\( 25 = 22 \)
Since \( 25 \neq 22 \), the formula does not hold true. Therefore, a polyhedron cannot have 10 faces, 20 edges, and 15 vertices simultaneously. Euler's formula must always be satisfied for a valid polyhedron.
In simple words: No, a polyhedron cannot have 10 faces, 20 edges, and 15 vertices. When we use Euler's rule \( F + V = E + 2 \), the numbers don't match up.

🎯 Exam Tip: Always use Euler's formula \( F + V = E + 2 \) to verify if a given set of faces, vertices, and edges can form a valid polyhedron.

IV. Short Answer Type Questions

 

Question 1. One vertex of a cube in cut equidistant from her three sides as shown in fig. How many faces and vertices
Answer: When one vertex of a cube is cut off equally from its three sides, it creates a new triangular face and modifies three existing square faces into irregular polygons.
Number of faces (F) = 7 (6 original faces - 3 modified + 1 new = 4 original + 3 modified + 1 new = 7)
Number of vertices (V) = 10 (8 original vertices - 1 removed + 3 new = 10)
The cut surface forms a new triangular face, adding one face. The original vertex is replaced by three new vertices where the cut meets the edges.
In simple words: If you slice off one corner of a cube, you add one new flat surface. This also changes the number of corners, so there will be 7 faces and 10 vertices.

🎯 Exam Tip: When a vertex is cut, it replaces one vertex with multiple new ones, and adds a new face to the solid. Keep track of the changes to existing faces as well.

 

Question 2. Can a polyhedron have for its faces
(i) 3 triangles?
(ii) 4 triangles?
(iii) a square and four triangles?
Answer: A polyhedron is a solid shape bounded by four or more flat polygonal faces. These faces meet along edges, and three or more edges meet at each vertex.
(i) It is not possible for a polyhedron to have only 3 triangles as its faces because a polyhedron needs at least four faces to enclose a space.
(ii) Yes, 4 triangles can be the faces of a polyhedron. An example is a triangular pyramid (tetrahedron), which has four triangular faces.
(iii) Yes, a square and four triangles can be the faces of a polyhedron. An example is a square pyramid, which has a square base and four triangular side faces.
In simple words: A polyhedron needs at least four faces. So, 3 triangles are not enough. But 4 triangles (like a triangular pyramid) or one square and four triangles (like a square pyramid) can form a polyhedron.

🎯 Exam Tip: Remember the minimum number of faces for a polyhedron (4) and visualize common polyhedrons like pyramids to understand their face compositions.

 

Question 3. Which are prisms among the following?
(i) A nail
(ii) An unsharpened pencil
(iii) A table weight
(iv) A box
Answer: Among the given options, only a box is a prism.
(iv) A box is a prism because it has two identical and parallel rectangular bases, and its lateral faces are also rectangles. A typical box is a rectangular prism.
In simple words: Out of the given items, only a box is a prism because its shape matches the definition of a prism, with two parallel, identical ends and rectangular sides.

🎯 Exam Tip: Identify prisms by looking for two congruent and parallel bases, with rectangular or parallelogram sides connecting them.

 

Question 4.
(i) How are prisms and cylinders alike?
(ii) How are pyramids and cones alike?
Answer:
(i) Prisms and cylinders are alike because a prism starts to look like a cylinder if the number of sides on its base becomes very large. As the number of sides increases, the polygonal base gets closer to being a circle.
(ii) Pyramids and cones are alike because a pyramid begins to look like a cone when the number of sides on its polygonal base becomes very large. This makes the base appear more circular and the triangular faces blend into a smooth curved surface.
In simple words: (i) Prisms become like cylinders if their bases have many, many sides, making them round. (ii) Pyramids become like cones if their bases also have many sides, making them round at the bottom and pointy at the top.

🎯 Exam Tip: Understand that cylinders and cones can be seen as limiting cases of prisms and pyramids, respectively, when the number of sides of their bases approaches infinity.

 

Question 5. Using Euler's formula find the missing numbers.
Answer: We use Euler's formula: \( F + V = E + 2 \).

**For Polyhedron A:**
Given: Vertices (V) = 6, Edges (E) = 12
We need to find Faces (F).
Using Euler's formula: \( F + V = E + 2 \)
\( F + 6 = 12 + 2 \)
\( F + 6 = 14 \)
\( F = 14 - 6 \)
\( F = 8 \)
So, Polyhedron A has 8 faces.
**For Polyhedron B:**
Given: Faces (F) = 5, Edges (E) = 9
We need to find Vertices (V).
Using Euler's formula: \( F + V = E + 2 \)
\( 5 + V = 9 + 2 \)
\( 5 + V = 11 \)
\( V = 11 - 5 \)
\( V = 6 \)
So, Polyhedron B has 6 vertices.
The missing numbers are 8 faces for Polyhedron A and 6 vertices for Polyhedron B. Euler's formula is a powerful tool for analyzing polyhedrons.
In simple words: We use Euler's special rule to find the missing numbers. For shape A, if it has 6 corners and 12 lines, it must have 8 flat surfaces. For shape B, if it has 5 flat surfaces and 9 lines, it must have 6 corners.

🎯 Exam Tip: Clearly state Euler's formula and show each step of substitution and calculation when solving for missing values in polyhedrons.

 

Question 6. Find number of edges in a polyhedron which have 9 vertices and 9 faces.
Answer: We need to find the number of edges (E) for a polyhedron with 9 vertices (V) and 9 faces (F).
Using Euler's formula: \( F + V = E + 2 \)
Substitute the given values:
\( 9 + 9 = E + 2 \)
\( 18 = E + 2 \)
Now, subtract 2 from both sides to find E:
\( E = 18 - 2 \)
\( E = 16 \)
Therefore, the polyhedron has 16 edges. This confirms the consistency of the properties using the fundamental formula.
In simple words: To find the number of edges, we use Euler's formula. If a shape has 9 flat surfaces and 9 corners, it must have 16 edges.

🎯 Exam Tip: Write down the known values (F and V) first, then clearly apply Euler's formula to solve for the unknown (E).

 

Question 7. In a polyhedron, number of faces is 5 and number of edges is 9. Find the number of vertices.
Answer: We need to find the number of vertices (V) for a polyhedron with 5 faces (F) and 9 edges (E).
We use Euler's formula: \( F + V = E + 2 \)
Substitute the given values:
\( 5 + V = 9 + 2 \)
\( 5 + V = 11 \)
Now, subtract 5 from both sides to find V:
\( V = 11 - 5 \)
\( V = 6 \)
Therefore, the polyhedron has 6 vertices. This calculation is a direct application of Euler's relationship for polyhedrons.
In simple words: Using Euler's formula, if a polyhedron has 5 flat surfaces and 9 lines, it will have 6 corners.

🎯 Exam Tip: Double-check your arithmetic, especially when rearranging the Euler's formula to solve for a specific variable.