ચોરસ પાયાવાળા પિરામિડના શિરોબિંદુV) , ધાર (E ) અને ફલક (F) ની સંખ્યા શોધો અને તે
આધારે યુલરનું સૂત્ર ચકાસો.
Answers
Given : pyramid with square base
ચોરસ પાયા વાળા પિરામિડના
To Find : number of faces, edges and vertices
Verify Euler Formula
શિરોબિંદુV) , ધાર (E ) અને ફલક (F) ની સંખ્યા શોધો
આધારે યુલરનું સૂત્ર ચકાસો.
Solution:
pyramid with square base
4 vertex of Square as base
and 1 vertex at top
=> Total Vertex V = 4 + 1 = 5
On Face is Square
4 faces are ( slanted ) of 4 triangles
Faces F = 1 + 4 = 5
Edges
4 - Edges of Square
3 Edges of one triangle hence 3 x 4 = 12 Edges
But 1 Edge of triangle is common with other triangle
and 1 Edge of triangle is common with Square
Hence 2 x 4 = 8 Edges to be reduced
Edges = 4 + 12 - 8 = 8
Vertex V = 5
Faces F = 5
Edges E = 8
Euler formula for faces
= Edges - Vertex + 2
=> F = E - V + 2
LHS = F = 5
RHS = E - V + 2
= 8 - 5 + 2
= 5
LHS = RHS = 5
Hence Verified
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Answer:
Step-by-step explanation:
