Q.2: For cub e sha pe pro ve the Euler's
Formula.
Sol utio n: In a tetr ahe dro n,
F= 6
V= 8
E = 12
Thu s, F+V-E
= 6+8-12
= 2
Hen ce pro ved .
,Solved Examples on Euler's
Formula
Q.1: For tet ra he dr on sh ap e pr ov e th e
Euler's Formula.
So lut ion : In a tet rah ed ron ,
FN urn be r of fac es, F = 4
Nu mb er of Ve rtic es, V= 4
Nu mb er of Ed ge s, E = 6
Th us, F+V-E
= 4+4-6
= 2.
He nc e pro ve d.
, Eu ler's for mu la sta tes for polyhedron
tha t the se will follow certain rules:
F+V-E=2
W he re,
F Num ber of faces
V Num ber of vert ices {Co rners)
E Num ber of edges
Euler's Formula for other shapes
Eu ler 's Fo rm ula does wo rk only for a
po lyh ed ro n wi th ce rta in rules. The rule
is tha t the sh ap e sh ou ld no t ha ve any
holes, an d also it mu st no t intersect
itself. Also, it also ca nn ot be ma de up of
tw o pie ce s stu ck together, like two
cu be s stu ck tog eth er by one vertex.
Formula.
Sol utio n: In a tetr ahe dro n,
F= 6
V= 8
E = 12
Thu s, F+V-E
= 6+8-12
= 2
Hen ce pro ved .
,Solved Examples on Euler's
Formula
Q.1: For tet ra he dr on sh ap e pr ov e th e
Euler's Formula.
So lut ion : In a tet rah ed ron ,
FN urn be r of fac es, F = 4
Nu mb er of Ve rtic es, V= 4
Nu mb er of Ed ge s, E = 6
Th us, F+V-E
= 4+4-6
= 2.
He nc e pro ve d.
, Eu ler's for mu la sta tes for polyhedron
tha t the se will follow certain rules:
F+V-E=2
W he re,
F Num ber of faces
V Num ber of vert ices {Co rners)
E Num ber of edges
Euler's Formula for other shapes
Eu ler 's Fo rm ula does wo rk only for a
po lyh ed ro n wi th ce rta in rules. The rule
is tha t the sh ap e sh ou ld no t ha ve any
holes, an d also it mu st no t intersect
itself. Also, it also ca nn ot be ma de up of
tw o pie ce s stu ck together, like two
cu be s stu ck tog eth er by one vertex.
