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MATHS [3 marks sum]

Representing 3-D in 2-D · ICSE STD 8 (ICSE - English Medium). 4 questions.

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[3 marks sum]

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4 questions · timed · auto-graded

Question 13 Marks
Can a polyhedron have $8$ faces, $26$ edges, and $16$ vertices?
Answer
Number of faces $= 8$
Number of vertices $= 16$
Number of edges $= 26$
Using Euler’s formula
$F + V – E$
$\Rightarrow 8 + 16 – 26 \neq -2$
$\Rightarrow -2 \neq 2$
No, a polyhedron cannot have $8$ faces, $26$ edges, and $16$ vertices.
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Question 23 Marks
If a polyhedron has $10$ vertices and $7$ faces, find the number of edges in it.
Answer
Vertices $= 10$
Faces $= 7$
Using Eulers formula,
$F + V – E = 2$
$7 + 10 – E = 2$
$-E = -15$
$E = 15$
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Question 33 Marks
If a polyhedron has $10$ faces and $8$ vertices, find the number of edges in it.
Answer
Faces $= 10$
Vertices $= 8$
using Eulers formula,
$F + V – E = 2$
$10 + 8 – E = 2$
$-E = 2 – 18$
$E= 16$
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[3 marks sum] - MATHS STD 8 Questions - Vidyadip