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)

	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