Complete the following table and verify Euler's formula in each case.
|Euler's formula (F − E + V)||6 − 12 + 8 = 2||4 − 6 + 4 = 2||9 − 16 + 9 = 2||7 − 15 + 10 = 2|
Hence Euler's formula is verified for these figures.
Give three examples from our daily life which are in the form of (i) a cone (ii) a sphere (iii) a cuboid (iv) a cylinder (v) a pyramid.
Match the following nets with appropriate solids:
(a) → (ii)
(b) → (iii)
(c) → (iv)
(d) → (i)
Identify the nets which can be used to make cubes (cut-out the nets and try it):
Only (ii), (iv) and (vi) form a cube.
Can the following be a net for a die? Explain your answer.
Since, in a die, the sum of the number of opposite faces of a die is 7. In the given figure, it is not possible to get the sum as 7. Hence the given net is not suitable for a die.
Out of the following four nets there are two correct nets to make a tetrahedron. Identify them.
For making a tetrahedron, only (i) and (iii) are suitable nets.
Here is an incomplete net for making a cube. Complete it in atleast two different ways.
The complete nets for making a cube are Images