**Exercise 10.1**

*Question 1: *

*Given below are solids, and their compared views. Match them by comparing them with their top views and front views. For the example default: The first is done for you:*

**Answer: **

** **

(1) \(\rightarrow\)iii)\(\rightarrow\)iv)

(2) \(\rightarrow\)i) \(\rightarrow\)v)

(3) \(\rightarrow\)iv)\(\rightarrow\)ii)

(4) \(\rightarrow\)v) \(\rightarrow\)iii)

(5) \(\rightarrow\)ii) \(\rightarrow\)i)

*Question 2:*

*The three views are given for the solids. Match these solids with given top, front and side views.*

** **

**Answer: **

(1)\(\rightarrow\)(i) \(\rightarrow\)F (ii) \(\rightarrow\) (iii)\(\rightarrow\)T

(2)\(\rightarrow\)(i) \(\rightarrow\) (ii)\(\rightarrow\)F (iii)\(\rightarrow\)T

(3)\(\rightarrow\)(i) \(\rightarrow\)F (ii)\(\rightarrow\)S (iii)\(\rightarrow\)T

(4)\(\rightarrow\)(i)\(\rightarrow\)F (ii)\(\rightarrow\)S (iii)\(\rightarrow\)T

*Question 3: *

*Using the solids given.Match the top view, side view and front view.*

**Answer: **

(a)\(\rightarrow\)(i) \(\rightarrow\)T (ii) \(\rightarrow\)F(iii)\(\rightarrow\)S

(b) \(\rightarrow\)(i) \(\rightarrow\)S (ii) \(\rightarrow\)F(iii)\(\rightarrow\)T

(c)\(\rightarrow\)(i)\(\rightarrow\)T (ii)\(\rightarrow\)S (iii) \(\rightarrow\)F

(d)\(\rightarrow\)(i) \(\rightarrow\)S (ii)\(\rightarrow\)F(iii)\(\rightarrow\)T

(e)\(\rightarrow\)(i)\(\rightarrow\)F(ii)\(\rightarrow\)T (iii)\(\rightarrow\)S

** **

*Question 4:*

* **In the given solids,draw top view, side view and front view.*

**Answer:**

*Exercise 10.2*

*Question 1: *

* **See the map and answer the questions correctly:*

** **

*Look at the given map of a city.*

* *

*Answer the following:*

* **a) Color the map by the following instructions: *

* **Water –Blue color*

*Fire station-Red color*

*Library -Orange color*

*Schools -Yellow color*

*Park-Green color*

*College-Pink color*

*Hospital -Purple color*

*Cemetery-Brown color*

* *

*(b) Mark the green ‘Z’ at the roads between the Road ‘S’ and Nehru Road, Green ‘W’ at the roads between the Gandhi Road and Road ‘R’.*

* *

*(c) In red, use pencil to draw a small street route from library to the bus stop.*

* *

*(d) Which is in the east of the map, the park or the city market?*

*(e) Which is in south of the map, the Primary School or the Sr. Secondary School?*

** **

**Activity Based Questions:**

*Question 1: *

*Draw a simple map of your classroom pathway by using proper scale, name it accordingly, and define it with given symbols.*

** **

*Question 2: *

*Draw a simple map of your class compound using proper scale and define symbols for various features like the playground, main gate building, beautiful garden etc.*

** **

*Question 3: *

*Draw a map by giving following instructions to your best friend so that she does not feel any difficulties while reaching your house.*

** **

**Exercise 10.3**

** **

**Question 1: **

**How many in number should a polygon have got for its face?**

**(i) Threetriangles **

**(ii) four triangles**

**(iii) A square & 4 triangles**

**Answer:**

** **(i)Not possible, a polyhedron do not have 3 triangles for its having no faces.

(ii)Yes, a polyhedron can also have 4 triangles which is also known as pyramid which is on a triangular base.

(iii)Yes, a polyhedron has the faces with a square and 4 triangles which makes a pyramid on its square base.

** **

*Question 2**: *

*Can any number of faces be added to a polyhedron (Hint: Think of a pyramid)*

* ***Answer: **

Yes, if only the number of faces is equal or more than 4.

** **

*Question 3:*

* **Which of the following is prism?*

** ****Answer: **

** **Figure (2) unsharpened pencil and (3) a box are the prisms.

** **

*Question 4: *

* **Give reasons:*

* **(i)Cylinders and prisms are same and alike.*

* **(ii)Cones and pyramid are same and alike.*

** ****Answer: **

** **(i)If the number of the sides in the prisms become much larger than the prisms tend to become cylinders.

(ii)When the number of the sides of the base increases then the pyramid tend to become a cone.

** **

*Question 5:*

* **Is square prism is equal to cube? Give reasons.*

** ****Answer:**

No, it is not possible; it can also be a shaped cuboid.

** **

*Question6: *

* **Give an adequate response of Euler’s formula for the given solids:*

** ****Answer: **

** **(i)Here, figure (i) Itcontains seven faces, ten vertices and fifteen edges.

Using Euler’s formula,

We tend to seeA + B

C = 2

Putting A = 7, B = 10 and C = 15,

A + B–C = 2

7 + 10–5 = 2

17 –15 = 2

2 = 2

L.H.S. = R.H.S.

(ii)Here, figure (ii) contains 9 faces, 9 Vertices and 16 edges.

Using Euler’s formula, we see

A + B–C = 2

A + B –C = 2

9 + 9 –16 = 2

18 –16 = 2

2 = 2

L.H.S. = R.H.S.

*Question7: *

* **Using Euler’s formula, find the unknown:*

** **

Faces |
? |
5 |
20 |

Vertices |
6 |
? |
12 |

Edges |
12 |
9 |
? |

**Answer:**

** **In first column,

A= ?, B = 6 and C = 12

Using Euler’s formula, we see A + B –C = 2

A + B –C = 2

A + 6 –12 = 2

A –6 = 2

A = 2 + 6 = 8

Hence there are 8 faces.

In second column,

A = 5, B= ? and C = 9

Using Euler’s formula, we see A + B –C = 2

A + B –C = 2

5 + B –9 = 2

B –4 = 2

B = 2 + 4 = 6

Hence there are 6 vertices.

In third column,

A = 20, B = 12 and C= ?

Using Euler’s formula, we see A + B–C= 2

A + B –C = 2

20 + 12 –C = 2

32 –C = 2

C = 32 –2 = 30

Hence there are 30 edges.

*Question 8: *

* **Can a polyhedron have 10 faces, 20 edges and 15 vertices?*

** ****Answer: **

** **If A = 10, B= 1

5 and C = 20.

Then, we know Using Euler’s formula, A+ B –C = 2

L.H.S.

= A + B –C = 10 + 15–20 = 25 –20 = 5

R.H.S. = 2

L.H.S. \(\neq\) R.H.S.

Therefore, it does not follow Euler’s formula