ML AGGARWAL CLASS 8 Chapter 17 Visualising Solid Shapes Exercise 17.2
Exercise 17.2
Question 1
Sol :
(i) No
(i) No
(ii) yes
(iii) yes
Question 2
Sol :
only (ii), (iv) are prisms
Question 3
Sol :
(i) Faces (F)=7
vertices (V)=10
Edges (E)}=15
Euler's Formula
F+V=E+27+10=15+217=17
∴ Euler's formula is Verified.
(ii) Faces (F)=9
vertices (v)=9
Edges (E)=16
Euler's formula
F+V=E+2
9+9=16+2
18=18
ஃ Euler's formula is verified.
(iii) Faces F=7
vertices (v)=7
Edges E=12
f+v=E+2
7+7=12+2
14=14
ஃ Euler's formula is verified.
(iv) Faces F)=9
vertices (v)=9
Edges (E)=16
f+V=E+2
9+9=16+2
18=18
ஃ Euler's formula is verified.
Question 4
Sol :
F=15
V=20
E=30
F-1 V=15+20=35
E+2=3008=32
F+V≠E+2
Violating Euler's formula
∴ Not possible
Question 5
Sol :
F=8
V=8
Euler's formula
F+V=E+28+8=E+216=E+2E=16−2E=14
∴ no.of edges =14
Question 6
Sol :
F=7
V=10
Euler's formula
F+V=E+27+10=E+2⋅17=E+2E=17−2E=15
Question 7
Sol :
(i) octahedral prism
Faces (F) = 10
Vertices (v) =16
Edges (E) = 24
(ii) Decagonal pyramid
Faces (F)=11
vertices (V)=11
Edges (E)=20
Question 8
Sol :
(diagram should be added)
Faces | Vertices | Edges | |
(i) | 6 | 8 | 12 |
(ii) | 5 | 5 | 8 |
(iii) | 14 | 24 | 36 |
(iv) | 12 | 16 | 30 |
(v) | 16 | 24 | 42 |
(vi) | 19 | 19 | 36 |
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