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Visualising Solid Shapes

Short Answer Type

41. A polyhedron is having 8 vertices and 12 edges. How many faces of it are there?

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42. A dodecahedron is having 20 vertices and 30 edges. How many faces are there?

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43. An icosahedron is having 20 triangular faces and 12 vertices. Find the number of its edges.

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44. What is the least number of planes that can enclose a solid? Name the simplest regular polyhedron and verify Euler’s formula for it.

At least 4 planes can form to enclose a solid. Tetrahedron is the simple polyhedron. Following figure represents a simplest solid, called tetrahedron.

A tetrahedron has:
4 triangular faces, i.e. F = 4
4 vertices, i.e. V = 4
6 edges, i.e. E = 6
Now, substituting the values of F, V and E in Euler's formula, i.e.
F + V = E + 2
we have
4 + 4 = 6 + 2

rightwards double arrow

8 = 8, which is true.
Thus, Euler's formula is verified for a tetrahedron.

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45. Name the figure shown here.
(i) How many faces does it have?
(ii) How many vertices does it have?
(iii) How many edges does it have?

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46.

Write the number of
(i) faces
(ii) edges
(iii) vertices for a triangular prism.

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47. Number of faces of a pyramid is 5. Find the number of its vertices when its edges are 8.

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48. What is Euler’s formula? Using Euler’s formula, find the number of faces of tetrahedron having vertices as 4 and 6 edges.

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49. What is a triangular pyramid? What is a pyramid called if its base is a square?

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50. A dice is a cube in which the number on the opposite faces must total 7. Draw its net.

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