**Exercise 19.1**

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**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

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**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.

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**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.

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**Question :5. Here is an incomplete net for making a cube. Complete it in at least two different ways.**

**Solution 5:**