Question

Find F, V and E for the following solids and verify Euler’s formula (i) Pentagonal based prism (ii) Hexagonal based prism (iii) Octagonal Pyramid.

Answer 1

(i) In a pentagonal based prism, both the base faces will be pentagons.

A pentagonal based prism can be drawn as follows:

F = 7

V = 10

E= 15

Euler’s Formula is F + V = E + 2

∴7 + 10 = 15 + 2

(ii) In a hexagonal based prism, both the base faces will be hexagons.

A hexagonal based prism can be drawn as follows:

F = 8

V = 12

E = 18

Euler’s Formula is F + V = E + 2

∴8 + 12 = 18 + 2

(iii) In an octagonal pyramid, the base face will be an octagon.

An octagonal pyramid can be drawn as follows:

F = 9

V = 9

E= 16

Euler’s Formula is F + V = E + 2

∴8 + 9 = 16 + 2