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MATHS 2 Marks Questions

Visualising Shapes · Gujarat Board (GSEB) STD 8 (GSEB - English Medium). 12 questions.

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12 questions · self-marked practice — reveal the answer and mark yourself.

Question 12 Marks
Verify Euler's formula for the following polyhedrons:
Answer
In the given polyhedron: Edges $E = 21$ Faces $F = 9$ Vertices $V = 14$

Now, putting these values in Euler's formula: $LHS: F + V = 9 + 14 = 23$
$RHS: E + 2 = 21 + 2 = 23$ This is true.
​​​​​​​Hence, Euler's formula is satisfied.
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Question 32 Marks
Dice are cubes where the numbers on the opposite faces must total $7.$ Which of the following are dice$?$
$i.$

$ii.$
Answer
Among the given figures, only figure $(i)$ is a dice. This is because if we fold the given net from the edges, we'll get a cube in which the sum of the opposite faces is $7.$
$ii.$
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Question 42 Marks
Is it possible to have a polyhedron with any given number of faces?
Answer
Yes, it is possible to have a polyhedron with any number of faces. The only condition is that there should be at least four faces. This is because there is no possible polyhedron with 3 or less faces.
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Question 62 Marks
Verify Euler's formula for the following polyhedrons:
Answer
In the given polyhedron: Edges $E = 16$ Faces $F = 9$ Vertices $V = 9$

Now, putting these values in Euler's formula:
$LHS: F + V = 9 + 9 = 18 $
$RHS: E + 2 = 16 + 2 = 18$
This is true. Hence, Euler's formula is satisfied.
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Question 92 Marks
Verify Euler's formula for the following polyhedrons:
Answer
In the given polyhedron:
Edges $E = 16$
Faces $F = 9$
Vertices $V = 9$

Now, putting these values in Euler's formula:
$LHS: F + V = 9 + 9 = 18 $
$RHS: E + 2 = 16 + 2 = 18$
This is true. Hence, Euler's formula is satisfied.
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Question 102 Marks
What is the least number of planes that can enclose a solid$?$ What is the name of the solid$?$
Answer
The least number of planes that can enclose a solid is $4.$ Tetrahedron is a solid with four planes (faces).
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Question 122 Marks
Verify Euler's formula for the following polyhedrons:
Answer
In the given polyhedron:
Edges $E = 15$
Faces $F = 7$
Vertices $V = 10$

Now, putting these values in Euler's formula:
$LHS: F + V = 7 + 10 = 17 $
$LHS: E + 2 = 15 + 2 = 17 $
$LHS = RHS$
Hence, the Euler's formula is satisfied.
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