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Question 2

For each of the given solid, the three views are given. Identify for each solid the corresponding top, front and side views.


Solution:




Question 3

For each given solid, identify the top views, front view and side view.

Solution:




Question 4

Can the faces polyhedron be
(i) 3 triangles (ii) 4 triangles (iii) a square and four triangles?

Solution:
(i) No (ii) Yes (iii) Yes



Solution:
If the number of faces more than 4 then it is possible.

Question 6

Which are prisms among the following?


Solution:


Question 7

(i) How are cylinder formed from a prism?
(ii) How are cones formed from pyramids?

Solution:
A prism becomes a cylinder as the number of sides becomes larger and larger.
As the sides of the pyramids becomes larger and larger, pyramids becomes a cone.


Question 8

Is a square prism is same as a cube? Explain.

Solution:
No, It is also a cuboid.


Question 9

Verify Euler's formula for these solids
Solution:
(i) Faces =7, Vertices = 10, Edges= 15
By Euler's formula, F + V - E = 2
                       7 + 10 − 15 = 17 − 15 = 2
Therefore, Euler's formula is verified.

(ii) Faces = 10, Vertices = 9, Edges = 16
By Euler's formula, F + V - E = 2
                       10 + 9 − 16 = 19 − 16 = 3 ≠ 2
Therefore, Euler's theorem is not true.


Question 10

Using Euler's formula find the unknown.

 
Faces ? 5 20
Vertices 6 ? 12
Edges 12 9 ?


Solution:
Euler's formula = F + V - E = 2
F + 6 - 12 = 2
        F - 6 = 2
               F = 8

5 + V - 9 = 2
      V - 4 = 2
             V = 6

20 + 12 - E = 2
       32 - 2 = E
              30 = E.


Question 11

Can a polyhedron have 10 faces, 20 edges and 15 vertices?

 


Solution:
No as Euler's formula is not true.




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