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

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

TSA (cube) =6 a²

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 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 :–

Return to- RS Aggarwal Solutions for ICSE Class-8 Goyal Brothers Prakashan


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