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Visualising Solid Shapes Exercise 19.1

Question: 1

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

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.


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