"Question 7 Using Euler’s formula, find the unknown.
Faces ? 5 20
Vertices 6 ? 12
Edges 12 9 ?
Class 8 Visualising Solid Shapes Page 167"
Answers
• Polyhedron: A three-dimensional figure whose faces are all polygons.
Regular polyhedrons: A polyhedron is said to be regular if its faces are made up of regular polygons and the same number of faces meet at each vertex.
• Prism: A polyhedron whose bottom and top faces (known as bases) are congruent polygons & faces known as lateral faces are parallelograms.
When the side faces are rectangles, the shape is known as right prism.
• Pyramid: A polyhedron whose base is a polygon and lateral faces are triangles
with a common vertex.
A prism or a pyramid is named after its base. Thus a hexagonal prism has a hexagon as its base; and a triangular pyramid has a triangle as its base
Face: A flat surface of a three dimensional figure.
Edge: Line segment where two faces of solid meet.
• Vertex: A point where three of more edges meet.
• Base: The face that is used to name a polyhedron.
Euler’s formula
• Euler’s formula for any polyhedron is F + V – E = 2, where F stands for number of faces, V for number of vertices and E for number of edges.
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Solution:
i)
Given:
V = 6
E = 12
F = ?,
Using Euler’s formula,
F + V – E = 2
F + 6 – 12 = 2
F – 6 = 2
F = 2 + 6 = 8
Hence there are 8 faces.
ii)
Given:
F = 5, E = 9
V = ?
Using Euler's formula,
F + V – E = 2
5 + V – 9 = 2
V – 4 = 2
V = 2 + 4 = 6
Hence there are 6 vertices.
iii)
Given:
F = 20, V = 12
E = ?
Using Euler's formula,
F + V – E = 2
20 + 12 – E = 2
32 – E = 2
E = 32 – 2 = 30
Hence ,there are 30 edges.
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Hope this will help you...