# RS Aggarwal Class-8 Three Dimensional Solids ICSE Maths Goyal Brothers

**RS Aggarwal Class-8 Three Dimensional** Solids ICSE Maths Goyal Brothers Prakashan Solutions Chapter-18. We provide step by step Solutions of Exercise / lesson-18 **Three Dimensional** Solids** ** for ICSE **Class-8 RS** **Aggarwal** Mathematics.

Our Solutions contain all type Questions of Exe-18 A, Exe-18 B, Exe-18 C, with Notes to develop skill and confidence. Visit official Website **CISCE** for detail information about ICSE Board Class-8 Mathematics.

**RS Aggarwal Class-8 Three Dimensional** Solids ICSE Maths Goyal Brothers Prakashan Solutions Chapter-18

**–: Select Topics :–**

**Notes on Three Dimensional Solids**

**Notes on Three Dimensional Solids**

Geometry is one of the practical sections of Mathematics which involves various shapes and sizes of different figures and their properties. Geometry can be divided into two types: **plane** and **solid** **geometry**. Plane geometry deals with flat shapes like lines, curves, polygons, etc., that can be drawn on a piece of paper. On the other hand, solid geometry involves objects of three-dimensional shapes such as cylinders, cubes, spheres, etc. Here we will discuss a few fundamental elements of solid geometry – the three-dimensional shapes.

#### What are Three-Dimensional Shapes?

Shapes which can be measured in 3 directions are called three-dimensional shapes. These shapes are also called solid shapes. Length, width, and height (or depth or thickness) are the three measurements of the three-dimensional shapes. They are a part of three-dimensional geometry. They are different from 2D shapes because they have thickness.

**Solid Shapes in Maths**

The three-dimensional objects having depth, width and height are called solid shapes. Let us consider a few shapes to learn about them. You can find many examples of solid shapes around you. The mobile, notebook or almost everything you can see around is a solid shape.

#### Surface Area and Volume of 3D shapes

The two distinct measures used for defining the 3D shapes are:

- Surface Area
- Volume

**Surface Area** is defined as the total area of the surface of the three-dimensional object. It is denoted as “SA”. The surface area is measured in terms of square units. The three different classifications of surface area are defined below. They are:

- Curved Surface Area (CSA) is the area of all the curved regions
- Lateral Surface Area (LSA) is the area of all the curved regions and all the flat surfaces excluding base areas
- Total Surface Area (TSA) is the area of all the surfaces including the base of a 3D object

**Volume** is defined as the total space occupied by the three-dimensional shape or solid object. The volume is denoted as “V”. It is measured in terms of cubic units

A cube is a solid or three-dimensional shape which has 6 square faces. The cube has the following properties.

- All edges are equal
- 8 vertices
- 12 edges
- 6 faces

The surface area and the volume of the cube are given below:

The Surface Area of a Cube = 6a^{2 }square units

The volume of a Cube **=** a^{3 } cubic units

### Cuboid

A cuboid also called a rectangular prism, where the faces of the cuboid are a rectangle in shape. All the angle measures are 90 degree

- 8 vertices
- 12 edges
- 6 faces

The surface area and the volume of the cuboid are given below:

The Surface Area of a Cuboid = 2(lb+bh+lh) Square units

The volume of a Cuboid **=** lbh Cubic units

### Cylinder

A cylinder is defined as the three-dimensional geometrical figure which has two circular bases connected by a curved surface. A cylinder has

- No vertex
- 2 edges
- 2 flat faces – circles
- 1 curved face

### Cone

A cone is a three-dimensional object or solid, which as a circular base and has a single vertex. The cone is a geometrical figure that decreases smoothly from the circular flat base to the top point called the apex. A cone has

- 1 vertex
- 1 edge
- 1 flat face – circle
- 1 curved face

The surface area and the volume of the cone are given below:

The Surface Area of a Cone = πr(r +√(r^{2}+h^{2}) Square units

Curved surface area of a cone =πrl

Slant height of a cone = l = √(r^{2}+h^{2})

The volume of a Cone **=** ⅓ πr^{2}h Cubic units

### Sphere

A sphere is a three-dimensional solid figure which is perfectly round in shapes and every point on its surface is equidistant from the point is called the centre. The fixed distance from the centre of the sphere is called a radius of the sphere. A sphere has

- No vertex
- No edges
- 1 curved face

The surface area and the volume of the sphere are given below:

The Curved Surface Area of a Sphere = 2πr² Square units

The Total Surface Area of a Sphere = 4πr² Square units

The volume of a Sphere **=** 4/3(πr^{3}) cubic units

**Exe-18 (A), RS Aggarwal Class-8 Three Dimensional** Solids ICSE Maths Goyal Brothers Prakashan Solutions

**Question 1 :**

Below are given in 3D solid and their deference view. Label the view shown as front view, side view and top view and tick the one which is the best 2D representation of the object shown

**Answer :**

**(i) **

(a) Front view

(b) Side view

(c) Top view

**(ii) **

(a) Top view

(b) Front view

(c) Side view

**(iii) **

(a) Front view

(b) Top view

**(iv) **

(a) Side view

(b) Top view

(c) Front view

**Question 2 :**

Complete the following table by filling the number of faces, the number of edges and the number of vertices for the given solid :

Solid | No. of Faces | No. of Edges | No. of Vertices |

(i) Cuboid | …………………….. | …………………….. | …………………….. |

(ii) Tetrahedron | …………………….. | ……………………… | …………………….. |

(iii) Rectangular Pyramid | …………………….. | …………………….. | …………………….. |

(iv) Pentagonal Pyramid | …………………….. | …………………….. | …………………….. |

(v) Hexagonal Pyramid | …………………….. | …………………….. | …………………….. |

(vi) Triangular Prism | …………………….. | …………………….. | …………………….. |

(vii) Pentagonal Prism | …………………….. | …………………….. | …………………….. |

(viii) Hexagonal Prism |
…………………….. | …………………….. | …………………….. |

**Answer :**

Solid | No. of Faces | No. of Edges | No. of Vertices |

(i) Cuboid | 6 | 12 | 8 |

(ii) Tetrahedron | 4 | 6 | 4 |

(iii) Rectangular Pyramid | 5 | 8 | 5 |

(iv) Pentagonal Pyramid | 6 | 10 | 6 |

(v) Hexagonal Pyramid | 7 | 12 | 7 |

(vi) Triangular Prism | 5 | 9 | 6 |

(vii) Pentagonal Prism | 7 | 15 | 10 |

(viii) Hexagonal Prism |
8 | 18 | 12 |

**Question 3 :**

** Fill in the blanks:**

(i) A Square prism may also be called ………………

(ii) A tetrahedron has …………………. triangular faces.

(iii) A pentagonal pyramid has …. ………… triangular faces.

(iv) The five lateral faces of a pentagonal prism are ………………

(v) Two adjacent faces of a solid meet in a / an ……………..

(vi) Two adjacent edges of a solid meet in a/an ………………

(vii) The side view of any pyramid depicts a ……………….

**Answer :**

(i) A Square prism may also be called **cuboid**

(ii) A tetrahedron has** 4** triangular faces .

(iii) A pentagonal pyramid has **5** triangular faces.

(iv) The five lateral faces of a pentagonal prism are **rectangle.**

(v) Two adjacent faces of a solid meet in a / an **edge.**

(vi) Two adjacent edges of a solid meet in a/an **vertex**

(vii) The side view of any pyramid depicts a **triangle.**

**Question 4 :**

Which of the following solids has the highest number of vertices ?

(i) Cuboid

(ii) Triangular Prism

(iii) Triangular Pyramid

(iv) Square Pyramid

**Answer :**

**(i) Cuboid**

**Question 5 :**

In which of the following solids, all the lateral faces are not triangular?

(i) Triangular Prism

(ii) Triangular Pyramid

(iii) Square Pyramid

(iv) Pentagonal Pyramid

**Answer :**

**(i) Triangular Prism**

**Question 6 :**

In which of the following solids, none of the faces is triangular?

(i) Triangular Prism

(ii) Square Pyramid

(iii) Pentagonal Pyramid

(iv) Hexagonal Prism

**Answer :**

**(iv) Hexagonal Prism**

**Question 7 :**

**Look at the following picture :**

Which of the option given below correctly represent the view of the above object as seen from the top ?

**Answer :**

(ii)

**Question 8 :**

**Choose the correct top view of the following jointed figure from the option given below it :**

** **

**Answer :**

**Question 9 :**

**Below are given three view of a 3d-jointed figure :**

** **

Choose the correct corresponding figure :

** **

**Answer :**

**Question 10:**

**Draw the correct 2D-front view of the jointed figure shown below :**

** **

**Answer :**

** **

**RS Aggarwal Class-8 Three Dimensional** Solids **Exe-18 (B),** ICSE Maths Goyal Brothers Prakashan Solutions

**Question 1 :**

Define Euler’s relation for 3-D figures.

**Answer :**

Euler’s relation = F – V + V = 2

where V= number of vertices

E = number of edge

and F = number of faces

**Question 2 :**

How many edge are there in a

(i) Cube

(ii) Triangular prism

(iii) tetrahedron

(iv) squire pyramid

**Answer :**

(i) Cube =12

(ii) Triangular prism = 9

(iii) tetrahedron =6

(iv) squire pyramid = 8

**Question 3 :**

How many faces are there in a

(i) cuboid

(ii) pentagonal prism

(iii) tetrahedron

(iv) hexagonal pyramid

**Answer :**

Faces of

(i) Cuboid are = 6

(ii) Pentagonal prism are = 7 (5+ 2)

(iii) Tetrahedron are = 4

(iv) Hexagonal pyramid are = 7

**Question 4 :**

How many vertices are there in a

(i) cube

(ii) triangular pyramid

(ii) square prism

(iv) triangular prism

**Answer :**

Vertices of

(i) Cube are = 8

(ii) Triangular pyramid are = 4

(ii) Square prism are = 8

(iv) Triangular prism are = 6

**Question 5 :**

**Verify Euler’s relation for each of the following:**

(i) cuboid

(ii) a triangular prism

(iii) a square pyramid

(iv) a tetrahedron

**Answer :**

(i) Cuboid

F – E + V = 2

6 – 12 + 8 = 2

14 – 12 = 2

2 = 2

(ii) A triangular prism

F – E + V = 2

5 – 9 + 6 = 2

11 – 9 = 2

2 = 2

(ii) A square pyramid

F – E + V = 2

5 – 8 + 5 = 2

10 – 8 = 2

2 = 2

(iv) A tetrahedron

F – E + V = 2

4 – 6 + 4 = 2

8 – 6 = 2

2 = 2

**RS Aggarwal Class-8 Exe-18 (C), Three Dimensional** Solids ICSE Maths Goyal Brothers Prakashan Solutions

**Question 1:**

Which solid figure would each of the following nets make when folded along dotted lines ?

** **

**Answer :**

(i) Cuboid

(ii) Triangular Prism

**Question 2:**

Which of these nets cannot be folded to form a cube ?

** **

**Answer :**

Not be Folded to form a cube are** (i), (iv), (vi), and (x)**

**Question 3:**

Which of the following four nets cannot be folded to form a square pyramid ?

**Answer :**

The nets cannot be folded to form a square pyramid is** **

**Question 4:**

Shown below is a cuboid on the square grid given below.

Draw a net for the cuboid on the square grid given below.

Each square is 1 cm x 1 cm.

** **

**Answer :**

** **

–: End of** RS Aggarwal Class-8 Three Dimensional** Solids Solutions :–

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