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All questions of Visualising Solid Shapes for Class 8 Exam

How many vertices does a cone have?
  • a)
    2
  • b)
    1
  • c)
    3
  • d)
    4
Correct answer is option 'B'. Can you explain this answer?

Aditi Saxena answered
When you have a two-dimensional shape like a cone, cube, cylinder, and rectangular prism, determining the amount of vertices becomes more complicated. You have to count the vertices from a three-dimensional angle 

Can you explain the answer of this question below:

How many congruent edges does a cube have?

  • A:

    12

  • B:

    6

  • C:

    8

  • D:

    none of these

The answer is A.

Shreya Bajaj answered
A line segment formed where two edges meet. A cube has 12 edges. Because all faces are squares and congruent to each other, all 12 edges are the same length.

Gaurav wants to make a pentagonal pyramid. How many triangles does he need to make the object?
  • a)
    2
  • b)
    3
  • c)
    5
  • d)
    4
Correct answer is option 'C'. Can you explain this answer?

Nandini Menon answered
Understanding a Pentagonal Pyramid
A pentagonal pyramid is a three-dimensional shape with a pentagon as its base and triangular faces that connect the vertices of the pentagon to a single apex (top point).
Components of a Pentagonal Pyramid
- Base Shape: The base of the pyramid is a pentagon, which has 5 sides.
- Apex: There is one apex from which all the triangular faces rise.
Triangles in a Pentagonal Pyramid
To construct a pentagonal pyramid, we need to determine how many triangular faces are required.
- Triangular Faces: Each side of the pentagon will have a triangular face that connects to the apex.
- Count of Triangles: Since the pentagon has 5 sides, it will have 5 triangular faces extending from each side to the apex.
Conclusion
Thus, Gaurav needs 5 triangles to create the pentagonal pyramid. Each triangle corresponds to a side of the pentagon, forming the complete structure.
Final Answer
The correct answer is option 'C': 5 triangles are required to make a pentagonal pyramid.

How many bases does a pyramid have?
  • a)
    4
  • b)
    2
  • c)
    1
  • d)
    3
Correct answer is option 'D'. Can you explain this answer?

Ashwin Jain answered
In the case of pyramid, these side faces are triangular with the faces meeting to form the vertex. You then add the three side faces with the base face to get four faces in total.

How many circular bases does a cylinder have?
  • a)
    2
  • b)
    3
  • c)
    4
  • d)
    1
Correct answer is option 'A'. Can you explain this answer?

Saanvi Kaur answered
A cylinder is similar to a prism, but its two bases are circles, not polygons. Also the sides of a cylinder are curved, not flat.
There are 2 circular bases 1 on top and 1 on bottom.

Identify the statement that is false for a prism. 
  • a)
    A right prism has rectangular lateral faces.
  • b)
    A right prism has two bases.
  • c)
    A right prism has triangular lateral faces.
  • d)
    A right prism has identical parallel faces.
Correct answer is option 'C'. Can you explain this answer?

Meera Yadav answered
False Statement: A right prism has triangular lateral faces.

Explanation:
A prism is a three-dimensional geometric figure that has two identical parallel bases and lateral faces that connect the corresponding vertices of the bases. The lateral faces are parallel to each other and are identical in shape. The bases of a prism are typically polygons, and the shape of the lateral faces depends on the shape of the bases.

A right prism is a type of prism where the lateral edges are perpendicular to the bases. In other words, the lateral faces form right angles with the bases. There are different types of right prisms, including rectangular prisms, triangular prisms, and pentagonal prisms, among others.

Let's analyze each statement to determine which one is false:

a) A right prism has rectangular lateral faces:
This statement is true. A right prism can have rectangular lateral faces. An example of a right prism with rectangular lateral faces is a rectangular prism or a cuboid.

b) A right prism has two bases:
This statement is true. A right prism always has two bases that are identical and parallel. These bases can be any polygon, such as a rectangle, triangle, or pentagon.

c) A right prism has triangular lateral faces:
This statement is false. A right prism does not have triangular lateral faces. Triangular lateral faces would make the prism a triangular prism, not a right prism. In a right prism, the lateral faces are parallel to each other and have the same shape as the bases.

d) A right prism has identical parallel faces:
This statement is true. A right prism has identical parallel faces. The bases are identical and parallel, and the lateral faces are also identical and parallel to each other.

Conclusion:
The false statement for a prism is option 'c' - A right prism has triangular lateral faces. A right prism does not have triangular lateral faces; instead, the lateral faces are parallel and have the same shape as the bases.

Find the side of a cube whose surface area is 2400 cm2.
  • a)
    20 cm
  • b)
    15 cm
  • c)
    10 cm
  • d)
    25 cm
Correct answer is option 'A'. Can you explain this answer?

Priya Nair answered
Surface area of  a cube = 6l2, where l is the length of its side
2400= 6l2
l= 2400/6
l2  = 400 = 202
l = 20 cm

An octagonal prism has ____.
  • a)
    24 edges and 16 vertices
  • b)
    20 edges and 16 vertices
  • c)
    24 edges and 15 vertices
  • d)
    15 edges and 11 vertices
Correct answer is option 'A'. Can you explain this answer?

Ritu Joshi answered
The correct answer is a) 24 edges and 16 vertices. 
An octagonal prism is a three-dimensional shape with eight flat faces that are all octagons. It has a total of 24 edges, since each of the eight faces has three edges and each edge is shared by two faces. It also has a total of 16 vertices, since each of the eight faces has four vertices and each vertex is shared by three faces.

Which is the three-dimensional figure formed by rotating a triangle?
  • a)
    Cone                                   
  • b)
    Quadrilateral
  • c)
    Prism                   
  • d)
    Square
Correct answer is option 'A'. Can you explain this answer?

Poulomi Shah answered
Rotating a Triangle
To understand which three-dimensional figure is formed by rotating a triangle, we need to consider the different possibilities.

A) Cone:
A cone is formed by rotating a right triangle around one of its legs. However, in this question, we are not given any specific information about the triangle being a right triangle or being rotated around one of its legs. Therefore, we can eliminate the option of a cone.

B) Quadrilateral:
A quadrilateral is a four-sided polygon, and rotating a triangle will not result in a quadrilateral. The rotation will either create a cone, a prism, or a square, so we can eliminate the option of a quadrilateral.

C) Prism:
A prism is formed by extending a polygon in one direction and then rotating it around that extension. In this case, if we rotate a triangle around one of its sides, we will not obtain a prism. Therefore, we can eliminate the option of a prism.

D) Square:
A square is a four-sided polygon with equal sides and right angles. When a triangle is rotated around one of its sides, the resulting figure will be a three-dimensional shape that has a circular base and a pointed top, like a cone. Therefore, the correct answer is option 'A' - Cone.

Conclusion:
When a triangle is rotated, the resulting figure will resemble a cone. Therefore, the answer to this question is option 'A' - Cone.

The faces of a pentagonal pyramid consist of
  • a)
    2 pentagons and 5 triangles
  • b)
    2 pentagons and 5 rectangles
  • c)
    one pentagon and 5 triangles
  • d)
    1 pentagon and 5 rectangles
Correct answer is option 'C'. Can you explain this answer?

Maya Nambiar answered
Firstly, we need to know the definition of the term “pentagonal pyramid”. From the name you can already guess it is something related to pentagon and also pyramid. So in geometry a pentagonal pyramid is a pyramid with a pentagon base upon which are erected fixed triangular faces that meet at a point.
So, from the diagram and definition, you can conclude that there is a base which is pentagonal shape that means a plane figure that has five straight sides. On every side a triangle is created upward. So, from five sides total five triangles are erected and meet at the point at top. So in total there are six faces of the pentagonal pyramid, one of the faces is a pentagon, which is in the base and the other five faces are a triangle hence  one pentagon and five triangles is the correct option.

A square pyramid always has ___.
  • a)
    Four lateral faces, which are parallel to each other.
  • b)
    Four lateral faces, which are congruent equilateral triangles and a rectangular base.
  • c)
    Two bases which are congruent and parallel.
  • d)
    Four lateral faces, which are congruent isosceles triangles and a square base.
Correct answer is option 'D'. Can you explain this answer?

Ameya Dasgupta answered
A square pyramid always has four lateral faces, which are congruent isosceles triangles and a square base.

A square pyramid is a type of pyramid where the base is a square and the lateral faces are triangles. Let's break down the characteristics of a square pyramid:

1. Square Base:
A square pyramid has a square base, which means all four sides of the base are equal in length and all four angles are right angles (90 degrees). The base provides stability and support for the pyramid.

2. Lateral Faces:
A square pyramid has four lateral faces that connect the vertices of the base to the apex (the top point of the pyramid). These lateral faces are triangles.

3. Congruent Isosceles Triangles:
The lateral faces of a square pyramid are congruent isosceles triangles. This means that two sides of each triangle are equal in length, and the angles opposite those equal sides are also equal. The congruent isosceles triangles form the slanted sides of the pyramid.

4. Apex:
The apex of a pyramid is the topmost point. In a square pyramid, the apex is directly above the center of the square base.

Summary:
In conclusion, a square pyramid always has a square base, four lateral faces that are congruent isosceles triangles, and an apex. It is important to understand the characteristics of a square pyramid to differentiate it from other types of pyramids.

How many triangles would you find in a net that folds into a square pyramid?  
  • a)
    3
  • b)
    4
  • c)
    5
  • d)
    6
Correct answer is option 'B'. Can you explain this answer?

Pyramid is that whose all lateral faces are triangles and Base is any Polygon .. since,Square pyramid will have 4 lateral faces so total no.s of triangle will be 4..

What do you call solid figures with line segments as their edges?
  • a)
    Polygons                            
  • b)
    Squares              
  • c)
    Cylinders           
  • d)
    Polyhedrons
Correct answer is option 'D'. Can you explain this answer?

The correct answer is option 'D' - Polyhedrons.
A polyhedron is a 3-dimensional solid figure with line segments as its edges. They have flat faces, and are defined by the number of faces, edges, and vertices. Some examples of polyhedrons include cubes, tetrahedrons, and octahedrons.

What is the shape of a sharpened pencil?
  • a)
    A cube surmounted on a cuboid.
  • b)
    A cone surmounted on a cylinder.
  • c)
    A triangle surmounted on a rectangle.
  • d)
    A triangle surmounted on a square.
Correct answer is option 'B'. Can you explain this answer?

  • A pencil is mostly cylindrical in shape (the body of the pencil).
  • When a pencil is sharpened, the tip forms a cone shape.
  • So, the overall shape of a sharpened pencil is a cylinder (body) with a cone (tip) on top.
  • What does the following figure represent?
    • a)
      A polygon
    • b)
      A convex polyhedron
    • c)
      A cylinder
    • d)
      A pyramid
    Correct answer is option 'B'. Can you explain this answer?

    A convex polyhedron is a three-dimensional solid with flat polygonal faces that doesn't intersect itself.
     
    Any line segment between two points inside the polyhedron is also inside the polyhedron.
     

    The faces of a triangular pyramid consist of
    • a)
      1 square and 3 triangles
    • b)
      2 triangles and 3 rectangles
    • c)
      4 triangles
    • d)
      2 rectangles and 3 triangles
    Correct answer is option 'C'. Can you explain this answer?

    Debolina Iyer answered
    There are 4 triangles in a triangular pyramid
    A triangular pyramid is a pyramid with a triangle as a base and three triangular faces. It has four vertices or points and six edges.

    Which of the following can be other name of a cylinder?
    • a)
      A triangular prism
    • b)
      A rectangular prism
    • c)
      A vertical prism
    • d)
      A circular prism
    Correct answer is option 'D'. Can you explain this answer?

    Poulomi Shah answered
    A circular prism is the correct answer because a cylinder is a three-dimensional geometric shape that has two parallel circular bases and a curved surface connecting the bases. It is similar in shape to a can of soda or a roll of paper towels.

    Explanation:

    Definition of a Cylinder:
    A cylinder is a three-dimensional figure that consists of two parallel circular bases connected by a curved surface. The bases are congruent and the axis connecting the centers of the bases is perpendicular to the bases.

    Alternative Names for a Cylinder:

    1. Circular Prism:
    A cylinder can be referred to as a circular prism because it has two circular bases that are parallel to each other. The term "prism" is often used to describe three-dimensional shapes with two congruent and parallel bases connected by rectangular or triangular sides. In the case of a cylinder, the sides are curved, but the concept is the same.

    2. Triangular Prism:
    A triangular prism is a three-dimensional shape that has two triangular bases connected by three rectangular sides. The shape of a triangular prism is different from a cylinder because it has triangular bases instead of circular bases.

    3. Rectangular Prism:
    A rectangular prism is a three-dimensional shape that has six rectangular faces. It is also different from a cylinder because it does not have circular bases or a curved surface.

    4. Vertical Prism:
    The term "vertical prism" is not commonly used to describe a cylinder. It is important to note that the orientation of a cylinder can vary, so it can be positioned vertically or horizontally. However, the term "vertical prism" does not accurately describe the shape of a cylinder.

    Therefore, the correct alternative name for a cylinder is a circular prism because it has two parallel circular bases connected by a curved surface.

    The base of a prism is an octagon. Find the total number of edges on the prism.
    • a)
      6
    • b)
      12
    • c)
      18
    • d)
      24
    Correct answer is option 'D'. Can you explain this answer?

    Malavika Basu answered
    An octagon is a polynomial with eight sides.

    An octagonal prism will have two octagonal faces i.e. a total of 8x2=16 sides as edges.

    And additionally all eight corners of one octagon will be connected to eight corners of other octagon, forming 8 edges.

    Hence total number of edges of an octagonal prism will be 16+8=24.

    What is the name of this solid?
    • a)
      a square prism
    • b)
      a tetrahedron
    • c)
      a cone
    • d)
      a square pyramid
    Correct answer is option 'D'. Can you explain this answer?

    Aditi Saxena answered
    A square pyramid is a pyramid, in geometry, that has a square base and four lateral faces. A Pyramid is a polyhedron that has a base and 3 or greater triangular faces that meet at a point above the base (the apex). A square pyramid is a three-dimensional shape that has a total of five faces, hence called a pentahedron.  A most famous example of such a pyramid in real life is the Great Pyramid of Giza.

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