Visualising Solid Shapes Exercise 19.1

Question: 1

Complete the following table and verify Euler’s formula in each case.

Face (F)	6	4
Edge (E)	12
Vertex (V)	8	4

Solution:

	I	II	III	IV
Face (F)	6	4	9	7
Edge	12	8	16	15
Vertex (V)	8	4	9	10
Euler's Formula (F - E + V)	6 - 12 + 8 =2	4 - 6 + 4 = 2	9 - 16 + 9 = 2	7 - 15 + 10 = 2

Hence Euler’s formula is verified for these figures.

 

Question: 2

Give three examples from our daily life which are in the form of

(i) A cone

(ii) A sphere

(iii) A cuboid

(iv) A cylinder

(v) A pyramid.

Solution:

Examples of

(i) Cone: Ice-cream cone, clown cap, rocket

(ii) Sphere: Football, a round apple, an orange

(iii) Cuboid: book, brick, duster

(iv) Cylinder: circular pipe, glass, circular pole

(v) Christmas decorations, cheese and patio umbrellas.