(1) For each of the given solid, the two views are given. Match for each solid the corresponding top and front views. The first one is done for you.

**Ans- **The corresponding top and front views are matched with object and presented below-

(2) For each of the given solid, the three views are given. Idetity for each solid the corresponding top, front and side views.

Ans- The corresponding top, front and side views for each of the given solid are presented below-

(3) For each given soild, identify th etop view, front view and side view.

Ans- The corresponding top, front and side views for each of the given solid are presented below-

(4) Draw the front view, side view and top view of the given objects.

**Ans-** The front view, side view and top view of the given objects are presented in the table below-

**Exercise 10.2**

**(1)** Look at te given map of teh city.

Answer the following.

**(a)** Colour the map as follows: blue – water, red – fire stattion, orange – library, yellow – schools, green – park, pink – college, purple- hospital, brown – cemetery.

**(b)** Mark a green ‘X’ at the intersection of Road ‘C’ and Nehru Road, Green ‘Y’ at the intersection of Gandhi Road and Road A.

**(c)** In red, draw a short street route from Library to the bus depot.

**(d)** Which is further east, the city park or the market?

**(e)** Which is further south, the primary school or the St. Secondary School?

Ans-

(a) The required map is showing below-

(b) Thge required mark of ‘X’ and ‘Y’ are showing below-

(c) The required path is showing below-

(d) The city park is at the further east.

(e) The St. Secondary School is at the further south.

**(2)** Draw a map of your class room using proper scale and symbols for different objects?

Ans- A map of class room is showing below-

(3) Draw a map of your school compound using proper scale and symbols for various features like play ground mail building, garden etc.

Ans- A map of school compound is showing below-

(4) Draw a map giving instructions to your friend so that she reaches your house without any difficulty.

Ans-A map giving instructions to my friend so that she reaches my house without any difficulty is showing below-

**Exercise 10.3**

**(1)** Can a polyhedron have for its faces

**(i)** 3 triangles? (ii) 4 triangles? (iii) a square and four triangles?

**Ans-**

**(i)** No, for polyhedron four faces are necessary.

**(ii)** Yes, for polyhedron four faces are necessary.

**(iii)** Yes, for polyhedron four faces are necessary.

**(2)** Is it possible to have a polyhedron with any given number of faces? ( Hint: Think of a pyramid)

**Ans-**

Yes, but number of faces should be 4 or more than 4 faces.

**(3)** Which are prisms among the following?

**(i) (ii)**

** A nail Unsharpened pencil**

**(iii) ****(iv) **

** A table weight A box**

**Ans-**

**(i) **A nail is not a prism because its base (point) and top (circle)are not congruent and other faces are not parallelogram.

**(ii)** An unsharpened pencil is a prism because top (hexagon) and base (hexagon) are congruent and other lateral sides are parallelogram.

**(iii)** A table weight is not a prism because its base (four sides) and top (point) are not congruent and other faces are not parallelogram.

**(iv)** A box is a prism because top (rectangle) and base (rectangle) are congruent and other lateral sides are parallelogram.

**(4) (i)** How are prisms and cylinders alike?

**(ii)** How are pyramids and cones alike?

**Ans-**

**(i)** Prisms and cylinders are alike because top and base of both are congruent.

**(ii)** Pyramids and cones are alike because base of pyramid is poygon and baso cone is circle.

**(5)** Is a square prism same as a cube? Explain.

**Ans-**

A square prism can be a cube or cuboid.

If a square prism has lateral sides square in shape with same measurements then it will be cube.

If a square prism has lateral sides not square in shape then it will be cuboid.

(6) Verify Euler’s formula for these soilds.

**(i)** **(ii)**

**Ans-**

Euler’s Formula faces (F), vertices (V) and edges (E) of polyhedron.

Euler’s Formula

F + V – E = 2

Where,

Faces = F

Vertices = V

Edges = E

**(i)**

Faces = 7

Vertices = 10

Edges = 15

F + V – E = 2

7 + 10 – 15 =2

2 = 2

LHS = RHS

Hence, Euler’s theorem proved.

**(ii)**

Faces = 10

Vertices = 9

Edges = 16

F + V – E = 2

10 + 9 – 16 =2

3≠ 2

LHS ≠ RHS

Hence, Euler’s theorem is not proved.

**(7)** Using Euler’s formula find the unknown.

Faces | ? | 5 | 20 |

Vertices | 6 | ? | 12 |

Edges | 12 | 9 | ? |

**Ans-**

Faces | 8 |
5 | 20 |

Vertices | 6 | 6 |
12 |

Edges | 12 | 9 | 30 |

When,

Faces = x

Vertices = 6

Edges = 12

F + V – E = 2

x + 6 -12 =2

x -6 = 2

x = 8

when,

Faces = 5

Vertices = x

Edges = 9

F + V – E = 2

5 + x – 9 =2

x – 4 = 2

x = 6

when,

Faces = 20

Vertices = 12

Edges = x

F + V – E = 2

20 + 12 – x =2

32 – x = 2

x = 30

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

**Ans-**

Faces = 10

Vertices = 15

Edges = 20

Euler’s Theorem

F + V – E = 2

LHS

=10 + 15 – 20

= 25 – 20

= 5

≠

RHS

No, a polyhedron can not have 10 faces, 20 edges and 15 vertices.

**Helping Topics**