Visualising Shapes Exercise 19.1

Question: 1

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

Solution:

	I	II	III	IV
Faces (F)	6	4	9	7
Edges (E)	12	6	16	15
Vertices (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) Pyramid: Christmas decorations, cheese and patio umbrellas.