3 Marks Question

Question 13 Marks

Verify Euler's relation for the following: A tetrahedron.

Answer

Euler's relation is: $F - E + V = 2$
A tetrahedron: Number of faces $= F = 4$
Number of edges $= E = 6$
Number of vertices $= V = 4$
$\Rightarrow (F - E + V) = 4 - 6 + 4 = 2$

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Question 23 Marks

Verify Euler's relation for the following: A cube.

Answer

Euler's relation is: $F - E + V = 2$
A cube: (There is an error in this question. It should have been a square prism rather than square.)
Number of faces $= F = 2$ squares + $4$ rectangular $= 6$
Number of edges $= E = 12$
Number of vertices $= V = 8$
$\Rightarrow (F - E + V) = 6 - 12 + 8 = 2$

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Question 33 Marks

Verify Euler's relation for the following: A triangular prism.

Answer

Euler's relation is: $F - E + V = 2$
A triangular prism: Number of faces $= F$
$= 2$ triangular + $3$ rectangular
$= 5$ Number of edges $= E = 9 $
Number of vertices $= V = 6$
$\Rightarrow (F - E + V) = 5 - 9 + 6 = 2$

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Question 43 Marks

Verify Euler's relation for the following: A square pyramid.

Answer

Euler's relation is: $F - E + V = 2$
A square pyramid: Number of faces $= F$
$= 2$ triangular + $3$ rectangular
$= 5$ Number of edges $= E$
$= 8$ Number of vertices $= V = 5$
$\Rightarrow (F - E + V) = 5 - 8 + 5 = 2$

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