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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?

Number of vertices (V) = 8
Number of edges (E) = 12
Let the number of faces = V
Now, using the Euler's formula
F + V = E + 2
we have
F + 8 = 12 + 2
$rightwards double arrow$ F + 8 = 14
$rightwards double arrow$ F = 14 - 8
$rightwards double arrow$ F = 6
Thus, the required number of faces = 6.

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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.

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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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