[5 marks sum] - MATHS STD 6 Questions - Vidyadip

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Question 15 Marks

Using Euler’s formula, find the values of a, b, c and d.

Faces	a	5	20	6
Vertices	6	b	12	d
Edges	12	9	c	12

Answer

Faces	a	5	20	6
Vertices	6	b	12	d
Edges	12	9	c	12

(i) a + 6 – 12 = 2
⇒ a = 2 – 6 + 12
= 14 – 6
= 8
(ii) b + 5 – 9 = 2
⇒ 6 = 2 + 9 – 5
= 6
(iii) 20 + 12 – c = 2
⇒32 – c = 2
⇒ c = 32 – 2
⇒ c = 30
(iv) 6 + d – 12 = 2
⇒ d – 6 = 2
⇒ d = 2 + 6
= 8

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Question 25 Marks

Look at the solids, drawn below, and fill the given chart.
(i)

Triangular pyramid
(ii)

Square pyramid
(iii)

Polyhedon	Faces(F)	Vertices(V)	Edges(E)	F - E + V
(a) Triangular pyramid
(b) Square pyramid
(c) Hexahedron
(d) Hexagonal prism

Answer

Polyhedon	Faces(F)	Vertices(V)	Edges(E)	F - E + V
(a) Triangular pyramid	4	4	6	2
(b) Square pyramid	5	5	8	2
(c) Hexahedron	8	6	12	2
(d) Hexagonal prism	8	12	18	2

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[5 marks sum] - MATHS STD 6 Questions - Vidyadip