Question

Complete the table given below:

S.No	Solid	Shape of Solid	Number of faces F	Number of Verticles V	Number of edges E	F + V	E + 2
a.	Cuboid
b.	Triangular Pyramid
c.	Square Pyramid
d.	Rectangular Pyramid
e.	Pentagonal Pyramid
f.	Hexagonal Pyramid
g.	Triangular Prism
h.	Square Prism
i.	Cube
j.	Pentagonal Prism
k.	Octagonal Prism
l.	Heptagonal Prism

Answer 1

By using Euler’s formula for polyhedron,

S.No	Solid	Shape of Solid	Number of faces F	Number of Verticles V	Number of edges E	F + V	E + 2
a.	Cuboid		6	8	12	6 + 8 = 14	12 + 2 = 14
b.	Triangular Pyramid		4	4	6	4 + 4 = 8	6 + 2 = 8
c.	Square Pyramid		5	5	8	5 + 5 = 10	8 + 2 = 10
d.	Rectangular Pyramid		5	5	8	5 + 5 = 10	8 + 2 = 10
e.	Pentagonal Pyramid		6	6	10	6 + 6 = 12	10 + 2 = 12
f.	Hexagonal Pyramid		7	7	12	7 + 7 = 14	12 + 2 = 14
g.	Triangular Prism		5	6	9	5 + 6 = 11	9 + 2 = 11
h.	Square Prism		6	8	12	6 + 8 = 14	12 + 2 = 14
i.	Cube		6	8	12	6 + 8 = 14	12 + 2 = 14
j.	Pentagonal Prism		7	10	15	7 + 10 = 17	15 + 2 = 17
k.	Octagonal Prism		10	16	24	10 + 16 = 26	24 + 2 = 26
l.	Heptagonal Prism		9	14	21	9 + 14 = 23	21 + 2 = 23