[4 marks sum]

Question 14 Marks

State, the number of faces, number of vertices and number of edges of: $(i)$ a pentagonal pyramid $(ii)$ a hexagonal prism

Answer

$(i)$A pentagonal pyramid
Number of faces $= 6$
Number of vertices $= 6$
Number of edges $= 10$
$(ii)$
A hexagonal prism
Number of faces $= 8$
Number of vertices $= 12$
Number of edges $= 18$

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Question 24 Marks

Using Euler's formula, find the values of $x,y,z.$

	Faces	Vertices	Edges
$(i)$	$x$	$15$	$20$
$(ii)$	$6$	$y$	$8$
$(iii)$	$14$	$26$	$z$

Answer

$(i)F + V - E = 2$
$\Rightarrow x + 15 - 20 = 2$
$\Rightarrow x - 5 = 2 $
$\Rightarrow x = 2 + 5 = 7$
$(ii)F + V - E = 2$
$\Rightarrow 15 + y - 26 = 2$
$\Rightarrow y - 11 = 2$
$\Rightarrow y = 2 + 11 $
$\Rightarrow y = 13$
$(iii)F + V - E = 2$
$\Rightarrow 14 + 26 - Z = 2$
$\Rightarrow -Z = 2 - 40 $
$\Rightarrow Z = 38$

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Question 34 Marks

Verify Euler$\ ’$s formula for the following three$-$dimensional figures:

Answer

$(i)$ Number of vertices $= 6$
Number of faces $= 8$
Number of edges $= 12$
Using Euler formula,
$F + V – E = 2$
$8 + 6 – 12 = 2$
$2 = 2$ Hence proved.
$(ii)$Number of vertices $= 9$
Number of faces $= 8$
Number of edges $= 15$
Using, Euler’s formula,
$F + V – E = 2$
$9 + 8 – 15 = 2$
$2 = 2$ Hence proved.
$(iii)$Number of vertices $= 9$
Number of faces $= 5$
Number of edges $= 12$
Using, Euler$\ ’$s formula,
$F + V – E = 2$
$9 + 5 – 12 = 2$
$2 = 2$ Hence proved.

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MATHS [4 marks sum]

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