SChand Composite Mathematics Class 7 Chapter 18 Visualising Solid Shapes Exercise 18A

  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