
In which polyhedron has faces, vertices and edges?
A) Cube
B) Sphere
C) Triangular Prism
D) Cone
Answer
390.3k+ views
Hint: We have to find which polyhedron has faces, vertices and edges. Polyhedron can be defined as a three- dimensional structure which is made up of a finite number of polygonal faces. Generally, polyhedrons are named according to the number of faces.
Complete step by step answer:
In Euclidean geometry a polyhedron can be defined as a three- dimensional structure which is made up of a finite number of polygonal faces and they are named according to the number of faces. The boundary which is in between the interior and the exterior of a solid is a polyhedron.
The polyhedron is made up of three parts namely Face, Vertex and Edge.
A face is a flat surface that makes up a polyhedron which is a regular polygon.
An edge is the region where the two flat surfaces meet to form a line segment.
A vertex which is also known as a corner is a point of intersection of the edges of the polyhedron.
Here, we have to find which polyhedron has faces, vertices and edges.
A cube is a polyhedron which has faces, vertices and edges and it has three squares that meet at each vertex.
Hence, Option (A) is correct.
Note:
A sphere has face, edge and vertex.
A triangular prism has faces, vertices and edges.
A cone has faces, edge and vertex.
In Euclidean geometry there is a theorem known as Euler theorem named after Leonhard Euler which gives us a relation between the number of faces, vertices and edges of any polyhedron. The formula is given by where denotes the number of faces, denotes the number of vertices and denotes the number of edges of polyhedrons.
Complete step by step answer:
In Euclidean geometry a polyhedron can be defined as a three- dimensional structure which is made up of a finite number of polygonal faces and they are named according to the number of faces. The boundary which is in between the interior and the exterior of a solid is a polyhedron.
The polyhedron is made up of three parts namely Face, Vertex and Edge.
A face is a flat surface that makes up a polyhedron which is a regular polygon.
An edge is the region where the two flat surfaces meet to form a line segment.
A vertex which is also known as a corner is a point of intersection of the edges of the polyhedron.
Here, we have to find which polyhedron has
A cube is a polyhedron which has

Hence, Option (A) is correct.
Note:
A sphere has
A triangular prism has
A cone has
In Euclidean geometry there is a theorem known as Euler theorem named after Leonhard Euler which gives us a relation between the number of faces, vertices and edges of any polyhedron. The formula is given by
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