Class 8 Exam > Class 8 Questions > An octagonal prism has ____.a)24 edges and 16...
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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?
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An octagonal prism has ____.a)24 edges and 16 verticesb)20 edges and 1...
The correct answer is a) 24 edges and 16 vertices.
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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.
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An octagonal prism has ____.a)24 edges and 16 verticesb)20 edges and 1...
Octagonal Prism
An octagonal prism is a three-dimensional geometric shape that has two parallel and congruent octagonal bases connected by eight rectangular faces. It is a type of prism because it has two identical polygonal bases and rectangular faces that connect them.
Edges and Vertices
To determine the number of edges and vertices in an octagonal prism, let's break down the components of this shape:
1. Octagonal Bases:
- An octagon is a polygon with eight sides and eight angles.
- Each vertex of the octagon is a point where two sides meet.
- An octagon has eight vertices.
- Since there are two identical octagonal bases in an octagonal prism, there are a total of 8 vertices for each base, giving us a total of 16 vertices.
2. Rectangular Faces:
- An octagonal prism has eight rectangular faces.
- Each rectangular face has four edges.
- Since there are eight rectangular faces in an octagonal prism, there are a total of 8 * 4 = 32 edges.
3. Edges Connecting the Bases:
- The two bases of an octagonal prism are connected by eight vertical edges.
- These vertical edges are perpendicular to the bases and connect each vertex of one base to the corresponding vertex on the other base.
- Since there are eight vertical edges connecting the bases, we add these to the total number of edges.
- 32 (rectangular faces) + 8 (vertical edges connecting bases) = 40 edges.
Therefore, an octagonal prism has 40 edges and 16 vertices.
Answer
The correct answer is option A: 24 edges and 16 vertices.
An octagonal prism is a three-dimensional geometric shape that has two parallel and congruent octagonal bases connected by eight rectangular faces. It is a type of prism because it has two identical polygonal bases and rectangular faces that connect them.
Edges and Vertices
To determine the number of edges and vertices in an octagonal prism, let's break down the components of this shape:
1. Octagonal Bases:
- An octagon is a polygon with eight sides and eight angles.
- Each vertex of the octagon is a point where two sides meet.
- An octagon has eight vertices.
- Since there are two identical octagonal bases in an octagonal prism, there are a total of 8 vertices for each base, giving us a total of 16 vertices.
2. Rectangular Faces:
- An octagonal prism has eight rectangular faces.
- Each rectangular face has four edges.
- Since there are eight rectangular faces in an octagonal prism, there are a total of 8 * 4 = 32 edges.
3. Edges Connecting the Bases:
- The two bases of an octagonal prism are connected by eight vertical edges.
- These vertical edges are perpendicular to the bases and connect each vertex of one base to the corresponding vertex on the other base.
- Since there are eight vertical edges connecting the bases, we add these to the total number of edges.
- 32 (rectangular faces) + 8 (vertical edges connecting bases) = 40 edges.
Therefore, an octagonal prism has 40 edges and 16 vertices.
Answer
The correct answer is option A: 24 edges and 16 vertices.
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An octagonal prism has ____.a)24 edges and 16 verticesb)20 edges and 16 verticesc)24 edges and 15 verticesd)15 edges and 11 verticesCorrect answer is option 'A'. Can you explain this answer?
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