# RS Aggarwal Class-8 Volume and Surface Area of Solids ICSE Maths Goyal Brothers

**RS Aggarwal Class-8 Volume** and Surface Area of Solids ICSE Maths Goyal Brothers Prakashan Solutions Chapter-24. We provide step by step Solutions of Exercise / lesson-24 **Volume** and Surface Area of Solids** **for ICSE **Class-8 RS** Aggarwal Mathematics.

Our Solutions contain all type Questions of Exe-24 (A), Exe-24 (B), MCQs Exe-24 (C) and Mental Maths with Notes to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-8 Mathematics

Board | ICSE |

Publications | Goyal brothers Prakshan |

Subject | Maths |

Class | 8th |

Chapter-24 | Volume & Surface Area of Solids |

Writer | RS Aggrawal |

Book Name | Foundation |

Topics | Solution of Exe-24.a, 24.b, 24.c and Mental Math |

Academic Session | 2021-2022 |

**RS Aggarwal Class-8 Volume** and Surface Area of Solids ICSE Maths Goyal Brothers Prakashan Solutions Chapter-24

–: Select Topics :–

Notes on **Volume** and Surface Area of Solids

**Notes** on **Volume** and Surface Area of Solids

#### Area

The space occupied by a two-dimensional flat surface is called area. It is measured in square units.

Generally, Area can be of two types

**(i) Total Surface Area**

**(ii) Curved Surface Area**

#### Total surface area

Total surface area refers to the area including the base(s) and the curved part.

#### Curved surface area (lateral surface area)

Refers to the area of only the curved part excluding its base(s).

#### Volume

The amount of space, measured in cubic units, that an object or substance occupies. Some shapes are two-dimensional, so it doesn’t have volumes. Example, **Volume of Circle** cannot be found, though Volume of the sphere can be. It is so because a sphere is a three-dimensional shape

### Formula’s of **Surface area and Volume of Solids**

#### Cuboid and its Surface Area

The surface area of a cuboid is equal to the sum of the areas of its six rectangular faces. Consider a cuboid whose dimensions are l × b × h respectively.

The total surface area of the cuboid (TSA) = Sum of the areas of all its six faces

TSA (cuboid) = 2(l × b) + 2(b × h) + 2(l × h) = 2(lb + bh + lh)

Lateral surface area (LSA) is the area of all the sides apart from the top and bottom faces.

The lateral surface area of the cuboid = Area of face AEHD + Area of face BFGC + Area of face ABFE + Area of face DHGC

LSA (cuboid) = 2(b × h) + 2(l × h) = 2h(l + b)

Length of diagonal of a cuboid =√(l² + b² + h²

#### Cube and its Surface Area

For a cube, length = breadth = height

Let Cube with side = a

Similarly, the Lateral surface area of cube = 4 a²

Note: Diagonal of a cube =√3 a

#### Cylinder and its Surface Area

Take a cylinder of base radius *r* and height *h* units. The curved surface of this cylinder, if opened along the diameter (*d* = 2*r*) of the circular base can be transformed into a rectangle of length 2πr and height *h* units. Thus

CSA of a cylinder of base radius *r* and height h = 2π × r × h

TSA of a cylinder of base radius *r* and height h = 2π × r × h + area of two circular bases

=2π × r × h + 2πr²

=2πr(h + r)

#### Right Circular Cone and its Surface Area

Consider a right circular cone with slant length *l*, radius *r* and height *h*

CSA of right circular cone = πrl

TSA = CSA + area of base = πrl + πr2 = πr(l + r)

#### Sphere and its Surface Area

For a sphere of radius *r*

Curved Surface Area (CSA) = Total Surface Area (TSA) = 4πr2

#### Volume of a Cuboid

Volume of a cuboid = (base area) × height = (lb)h = lbh

#### Volume of a Cube

Volume of a cube = base area × height

Since all dimensions of a cube are identical, volume = l3

Where *l* is the length of the edge of the cube.

#### Volume of a Cylinder

Volume of a cylinder = Base area × height = (πr²) × h = πr²h

### Volume of a Right Circular Cone

The volume of a Right circular cone is 1/3 times that of a cylinder of same height and base.

In other words, 3 cones make a cylinder of the same height and base.

The volume of a Right circular cone =(1/3)πr²h

Where *r* is the radius of the base and *h* is the height of the cone.

### The volume of a Sphere

The volume of a sphere of radius *r* = (4/3)πr³

#### Hemisphere and its Surface Area

A hemisphere is half of a sphere.

∴ CSA of a hemisphere of radius *r* = 2πr2

Total Surface Area = curved surface area + area of the base circle

⇒TSA = 3πr²

### Volume of Hemisphere

The volume (V) of a hemisphere will be half of that of a sphere.

∴ The volume of the hemisphere of radius *r* = (2/3)πr³

**Exe-24 (A),** **RS Aggarwal Class-8 Volume** and Surface Area of Solids ICSE Maths Goyal Brothers Prakashan Solutions

(Page-294-295)

#### Question 1:

Find the volume, the total surface area and the ………………. having :

………………

#### Question 2:

Find the capacity of a rectangular ……………………… make the cistern.

#### Question 3:

A wall of length 13.5 m, ……………. bricks will be needed ?

#### Question 4:

…………………….

…………………….

…………………….

#### Question 24:

Three cubes of metal with …………….. new cube formed.

**Class-8 Volume** and Surface Area of Solids **Exe-24-(B), **ICSE Maths Goyal Brothers Prakashan Solutions

(Page 299-300)

#### Question 1:

Find the volume of the cylinder in which :

(i) height = 42 cm and base radius = 10 cm.

(ii) diameter = 70 cm and height = 20 m

#### Question 2:

Find the curved surface …………….. for which .

…………………….

#### Question 3:

Find the weight of solid ………………… gram per cm³

#### Question 4:

………………………

………………………

……………………….

#### Question 11:

A well with 10 m inside diameter is dug 8.4m deep. Earth taken ………….. Find the height of the embankment.

### **MCQs Exe-24 (C)**, of **RS Aggarwal Class-8 Volume** and Surface Area of Solids

(Page 300-301)

#### Question 1:

If the length, breadth and height of a cuboid ……………. area is

………………….

#### Question 2:

If the length …………… of the cuboid is

………………..

#### Question 3:

……………………

…………………….

…………………….

#### Question 28:

The number of coins 1.5 cm in diameter and 0.2 cm thick to be melted ……………….. 4.5 cm, is

**Mental Maths**

**RS Aggarwal Class-8 Volume** and Surface Area of Solids ICSE Maths Goyal Brothers Prakashan Solutions

#### (Page 302)

#### Question 1:

Fill in the blanks :

…………………..

…………………….

#### Answer :

(i) 1000000

(ii) 0.001

(iii) 6

(iv) Area

(v) Rectangle

(vi) 2 units.

–: End of **RS Aggarwal Class-8 Volume** and Surface Area of Solids Solutions :–

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