Exercise 19.1
Question :1. Complete the following table and verify Euler’s formula in each case.
Solution 1:
According to Euler’s formula is (F – E + V)
(i) (F – E + V)
= (6 – 12 + 8) = 2
So, Euler’s formula is verified
(ii) (F – E + V)
= (4 – E + 4) = 2.
E = 6
So, Euler’s formula is verified
(iii) (F – E + V)
= (9 – 16 + 9) = 2.
So, Euler’s formula is verified
(iv) (F – E + V)
= (7 – 15 + 10) = 2.
So, Euler’s formula is verified
Question :2. 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.
Solution 2:
(i) A Cone: Party hat, Ice cream cone, Christmas tree.
(ii) A Sphere: Ball, Planets, Moon.
(iii) A Cuboid: Bricks, Book, Mattresses.
(iv) A Cylinder: Pipes, Cold drink cans, Battery
(v) a Pyramid: Christmas tree, prism, piece of cake
Exercise 19.2
Question :1. Match the following nets with appropriate solids:
Solution 1:
Question :2. Identify the nets which can be used to make cubes (cut-out the nets and try it):
Solution 2:
(ii), (iv) and (vi) form a cube.
Question :3. Can the following be a net for a die? Explain your answer.
Solution 3:
We know that in a die, the sum of the number of opposite faces of a die is 7. In the specified figure, it is not possible to get the sum as 7. As a result, the given net is incompatible with a die.
Question :4. Out of the following four nets there are two correct nets to make a tetrahedron. Identify them.
Solution 4:
For making a tetrahedron, (i) and (iii) are suitable nets.
Question :5. Here is an incomplete net for making a cube. Complete it in at least two different ways.
Solution 5:
