Let ABCDHEFG be plasticine cube. Let a part xyz be sliced off from it. Let x, y, z lie on edge FG, FE and FB respectively.Case I. In cube ABCDHEFG,
F = 6
V = 8
E = 12
Clearly, F + V = E + 2 (= 14)
Thus, Euler's Formula is true.

Case II. When a part XYZ is sliced
Then, F = 7
V = 10
E = 15
Clearly, F + V = E + 2 (- 17)
Thus, Euler's Formula is again true

The top view of the glass is a pair of concentric circles because its top is a circle as well as its base is a concentric circle of smaller radius.
Due to symmetry, the side view will not appear different if taken from some other direction.

Required fraction
=\(\frac { 0.5 }{ 100 } \frac { 5 }{ 1000 } \)
=\(\frac { 5\div 5 }{ 1000\div 5 } =\frac { 1 }{ 200 } \)
H.C.F. (15,200) = 5

The woodcutter will have to cut only two times to make 3 pieces and four times to make 5 pieces.
=> Required time = 12 x 2 = 24 minutes

Let the number of five-rupee coins be x.
Then, number of two-rupee coins = 2x
∴ Total money
=5xx+2x2x
=5x + 4x = Rs. 9x
According to the question,
9x=108\(\Rightarrow \)x=\(\frac { 108 }{ 9 } \)
=> x = 12 => 2x = 2 x 12 = 24
Hence, I have 12 five-rupee coins and 24 two-rupee coins.

Let the number be x.
Then, according to the question,
6x+4=64 => 6x=64-4
\(\Rightarrow \)6x = 60 \(\Rightarrow \)x=\(\frac { 60 }{ 6 } \)
\(\Rightarrow \)x = 10
Hence, the required number is 10.

Four

Cube

Given, dimensions of two cuboid
3 cm x 3 cm x 6 cm.
Dimensions of the resulting figure are:
Height = 6 + 6 = 12 cm
Breadth = 3 cm
Length = 3 cm

Different sections of 3-D can be viewed in many ways as follows :
(i) One way is to view by cutting or slicing the shape, which would result in the cross-section of the solid.
(ii) Another way is by observing a 2-D shadow of a 3-D shape.
(iii) A third way is to look at the shape from different angles.

Faces = 6, edges = 12, vertices = 8

No, it is not possible, because one pair of opposite faces will have 1 and 4, whose total is not equal to 7 and another pair of opposite faces will have 3 and 6, whose total is not equal to 7

We know that, an oblique sketch does not have proportional lengths but it conveys all important aspects of the appearance of the solid. So, oblique sketch for each one of the given isometric sketch are as follow:

A cube has six faces, so complete net for making a cube in atleast two different ways are as follow:

In the given net, there are 6 faces of a cube.