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

Exe-24 (A),

Exe-24 (B),

MCQs Exe-24 (C),

Mental Maths

### 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 × × h respectively.

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

TSA (cuboid) = 2(× b2(× h2(× h2(lblh)

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(× h2(× h2h(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 = 2r) 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 2π × × h

TSA  of a cylinder of base radius r and height 2π × × h + area of two circular bases
=2π × × 2π
=2πr(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 πrπrπr(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× heigh(lb)lbh

#### Volume of a Cube

Volume of a cube = base are× 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 = (π× πh

### 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)πh
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)π

#### 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 3π

### 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)π

### 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 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 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 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

#### Question 1:

Fill in the blanks :

…………………..

…………………….

(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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