Exercise 18 A
Question 1
Leonhard Euler (1707-83) was a famous mathematician who discovered a rule about solids.-He observed the number of faces, vertices and edges of many solids before discovering this rule.
(a) Let us see if you can derive the Euler's rule $(F+V-E=2$ ) by completing the following table.
(Diagram to be added)
Question 2
For each solid, count the number of faces, vertices and edges. Check the Euler's rule for each one.
(Diagram to be added)
(a) (Diagram to be added)
Sol: F= 7
V=10
E=15
F+V-F=2
17-15=2
(b) (Diagram to be added)
Sol: $F=6$
$V=8$
$E=12$
$F+V-E$
$6+6-12$
$14-12$ = 2
(c) (Diagram to be added)
Sol:
$\begin{aligned} F &=7 \\ V &=7 \\ E &=12 \\ 14-12 \\ &=2 \end{aligned}$
(d) (Diagram to be added)
Sol: $F=9$
$V=9$
$E=16$
$18-16$
$=2$
Question 3
Fill in the blanks. Name a solid that has :
(i) 4 faces
(ii) 4 vertices
(iii) 2 edges
(iv) 6 vertices
(v) No edges.
(vi) 6 faces.
(Diagram to be added)
Multiple choice question
Question 4
Which of these solids has the maximum number of vertices ?
(a) Cons
(b) Cylinder
(c) Cuboid
(d) Pyramid
Question 5
If $\mathrm{F}=6$ and $\mathrm{V}=4$, then the value of $\mathrm{E}$ using Euler's formula is
(a) 10
(b) 8
(c) 2
(d) 4
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