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Visualising Solid Shapes

Short Answer Type

31. A polyhedron has 4 faces and 6 edges. Find the number of its vertices.

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32. A polyhedron has 5 faces and 6 vertices. How many edges will it have?

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Long Answer Type

33. Define the following:
(i) Polyhedron (ii) Prism (iii) Pyramid

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Short Answer Type

34. What is a polyhedra?

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35. What is a tetrahedron?

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36. What is a parallelopiped?

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Long Answer Type

37. Which of the following solids are not polyhedrons?

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Short Answer Type

38. Why the following solids are not polyhedron?
(i) A sphere.
(ii) A cone.
(iii) A cylinder.

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39. Name the following polyhedron.

How many faces, vertiecs and edges of this solid are there?

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40. What Euler’s formula? Verify the Euler’s formula for a pentagonal prism.

If a polyhedron is having number of faces as F, number of edges as E and the number of vertices as V, then the relationship F + V = E + 2 is known as Euler’s formula. Following figure is a solid pentagonal prism.

It has:
Number of faces (F) = 7
Number of edges (E) = 15
Number of vertices (V) = 10
Substituting the values of F, E and V in the relation,
F + V = E + 2
we have
7 + 10 = 15 + 2
$rightwards double arrow$ 17 = 17
Which is true, the Euler’s formula is verified.

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