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MATHS 3 Marks Question

Visualising Shapes · Rajasthan Board (RBSE) STD 8 (Rajasthan - English Medium). 3 questions.

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Question 13 Marks
Which among the following are nets for a cube?
Answer
To create a cube, we need six equal faces that enclose a closed box. In the given figure, only $(iv), (v)$ and $(vi)$ are such nets that enclose a box when we fold each face from the edge.
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Question 23 Marks
Can a polyhedron have $10$ faces, $20$ edges and $15$ vertices$?$
Answer
No, because every polyhedron satisfies Euler's formula, given below: $F + V = E + 2$
 Here, number of faces $F = 10$
Number of edges $E = 20$
Number of vertices $V = 15$
So, by Euler's formula: $LHS: 10 + 15 = 25$
 $RHS: 20 + 2 = 22$, which is not true because $25\neq22$
Hence, Eulers formula is not satisfied and no polyhedron may be formed.
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Question 33 Marks
Is a square prism same as a cube$?$
Answer
Yes, a square prism and a cube are the same.
Both of them have $6$ faces, $8$ vertices and $12$ edges.
The only difference is that a cube has $6$ equal faces, while a square prism has a shape like a cuboid with two squarefaces, one at the top and the other at the bottom and with, possibly, $4$ rectangular faces in between.
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