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Answer :

(i) In this given figure we have,

F = 7, V = 10, E =15

∴ F + V =7 + 10 = 17 and E + 2 =15 + 2 = 17

\(\Rightarrow\) F+V=E+ 2

Thus, Euler’s formula is verified.

(ii) In this given figure,

F =9, V = 9,E =16

∴ F + V =9 + 9 =18 and E + 2 =16 +2 =18

\(\Rightarrow\) F + V =E + 2

Thus, Euler’s formula is verified.

- 1.Can a polyhedron have for its faces (i) 3 triangles? (ii) 4 triangles? (iii) a square and four triangles?
- 2.Is it possible to have a polyhedron with any given number of faces? (Hint : Think of a pyramid)
- 3.Which are prisms among the following ?
- 4.(i) How are prisms and cylinders alike? (ii) How are pyramids and cones alike?
- 5.Is a square prism same as a cube? Explain.
- 7.Using Euler’s formula find the unknown.
- 8.Can a polyhedron have 10 faces, 20 edges and 15 vertices?

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