ML AGGARWAL CLASS 8 Chapter 17 Visualising Solid Shapes Exercise 17.2

 Exercise 17.2

Question 1

Sol :
(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

$\begin{aligned} F+V &=E+2 \\ 7+10 &=15+2 \\ 17 &=17 \end{aligned}$

$\therefore$ 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

$F+V \neq E+2$

Violating Euler's formula

$\therefore$ Not possible


Question 5

Sol :

F=8
V=8

Euler's formula

$\begin{aligned} F+V &=E+2 \\ 8+8 &=E+2 \\ 16 &=E+2 \\ E &=16-2 \\ E &=14 \end{aligned}$

$\therefore$ no.of edges =14

Question 6

Sol :
F=7
V=10

Euler's formula

$\begin{aligned} F+V &=E+2 \\ 7+10 &=E+2 \\ \cdot 17 &=E+2 \\ E &=17-2 \\ E &=15\end{aligned}$


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)

FacesVerticesEdges
(i)6812
(ii)558
(iii)142436
(iv)121630
(v)162442
(vi)191936

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