**Class 8 Maths Chapter 10 Visualising Solid Shapes**

**NCERT Solutions For Class 8 Maths Chapter 10 Visualising Solid Shapes, (Maths) exam are Students are taught thru NCERT books in some of state board and CBSE Schools. As the chapter involves an end, there is an exercise provided to assist students prepare for evaluation. Students need to clear up those exercises very well because the questions withinside the very last asked from those. **

**Sometimes, students get stuck withinside the exercises and are not able to clear up all of the questions. To assist students, solve all of the questions and maintain their studies without a doubt, we have provided step by step NCERT Solutions for the students for all classes. These answers will similarly help students in scoring better marks with the assist of properly illustrated Solutions as a way to similarly assist the students and answering the questions right.**

**NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes **

**Class 8 Maths Chapter 10 Visualising Solid Shapes**

**Exercise-10.1**

Page No: 157

**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.**

Solution.

(a) (iii) – (iv)

(b) (i) – (v)

(c) (iv) – (ii)

(d) (v) – (iii)

(e) (ii) – (i)

**2. For each of the given solid, the three views are given. Identify for each solid the corresponding top, front and side views.**

Solution.

(a) (i) Front (ii) Side (iii) Top view

(b) (i) Side (ii) Front (iii) Top view

(c) (i) Front (ii) Side (iii) Top view

(d) (i) Front (ii) Side (iii) Top view ** **

**3.For each given solid, identify the top view, front view, and side view.**

Solution.

(a) (i) Top view (ii) Front view (iii) Side view

(b) (i) Side view (ii) Front view (iii) Top view

(c) (i) Top view (ii) Side view (iii) Front view

(d) (i) Side view(ii) Front View(iii) Top view

(e) (i) Front view(ii) Top view(iii) Side view

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

Solution.

**Exercise 10.2**

Page No: 157

**1.Look at the given map of a city.**

**Answer the following.****(a)**Colour the map as follows: Bluewater, Red-fire station, Orange-Library, Yellow-schools, Green-Parks, Pink-Community Centre, 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 Sr. Secondary School?

**Solution.(a)** Please color yourself.

**(b)**See the above figure.

**(c)**See the above figure.

**(d)**City Park.

**(e)**Senior Secondary school.

**2.****Draw a map of your classroom using a proper scale and symbols for different objects.Solution.**Please draw yourself.

**3. ****Draw a map of your school compound using a proper scale and symbols for various features like playground main building, garden etc.Solution.**Please draw yourself.

**4.**** Draw a map giving instructions to your friend so that she reaches your house without any difficulty.Solution.**Please draw yourself.

## **Exercise 10.3**

**Page No: 166**

**1. Can a polyhedron have for its faces****(i)** 3 triangles?**(ii)** 4 triangles?**(iii)** a square and four triangles?**Solution.****(i) **No, such polyhedrons are not possible. Such figures should have minimum 4 faces.

**(ii)**Yes, a triangular pyramid has 4 triangular faces.

**(iii)**Yes, as square pyramid has a square face and 4 triangular faces

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

it is possible, only if the number of faces is greater than or equal to 4.

**3. Which are prisms among the following?**

**Solution.**i) A nail: Not a polyhedron as it has a curved surface. This is not a prism.

ii) Unsharpened Pencil: it is a prism.

iii) A table Weight: It is not a prism.

iv) A Box: It is a prism

**4.(i)**** **How are prisms and cylinders alike?** (ii)** How are pyramids and cones alike?**Solution.****(i)** The prisms and cylinder, both, have their base and top faces as congruent and parallel to each other. Also, a prism becomes a cylinder as the number of sides of its base becomes larger and larger.

**(ii)** The pyramids and cones are alike in the sense that their lateral faces meet at a point (called vertex). Also, a pyramid becomes a cone as the number of sides of its base becomes larger and larger.

**5. ****Is a square prism same as a cube ? Explain.Solution.**yes, a square prism can also be a cube. A square prism has a square as its base. However, its height is not necessarily same as the side of the square. Thus, a square prism can also be a cuboid.

**6.** **Verify Euler’s formula for these solids**

**Solution.(i)**Number of faces, F = 7 Number of edges, E = 15 Number of vertices, V = 10 As per formula, F + V – E = 2 Substitute the values, we have F + V – E = 7+10-15 = 2 Verified.

**(ii)**Here F = 9

V = 9

E = 16

Using formula, F+ V- E = 2 F+ V- E = 9+9-16 = 2 Hence, Euler’s Formula is verified

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

Faces | ? | 5 | 20 |

Vertices | 6 | ? | 12 |

Edges | 12 | 9 | ? |

**Solution.****(i)**Euler’s formula: F + V = E + 2

⇒ F + 6 = 12 + 2

⇒ F + 6 = 14

⇒ F = 14 – 6 = 8

**(ii)**

Euler’s formula: F + V = E + 2

⇒ 5 + V = 9 + 2

⇒ 5 + V = 11

⇒ V= 11-5 = 6

**(iii)**Euler’s formula: F + V = E + 2

⇒ 20 + 12 = E + 2

⇒ 32 = E + 2

⇒ E = 32 – 2

⇒ E = 30

**8.** **Can a polyhedron have 10 faces, 20 edges, and 15 vertices?Solution.**From the given data, we have

F=10 E = 20 V=15 Every polyhedron satisfies Euler’s formula, which is stated as, F + V E=2 For the given polygon, F + V – E = 10 + 15 – 20 = 25 – 20 = 5, which is not equal to 2 Therefore, A polyhedron is not possible as Euler’s formula is not satisfied.

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