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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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