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Surface Areas And Volumes Class 9th Notes - Free NCERT Class 9 Maths Chapter 13 Notes - Download PDF

Surface Areas And Volumes Class 9th Notes - Free NCERT Class 9 Maths Chapter 13 Notes - Download PDF

Edited By Ramraj Saini | Updated on Apr 21, 2022 01:13 PM IST

Surface Areas And Volumes Class 9th Notes:

The complete surface area and volume formulas for various three-dimensional shapes are discussed in NCERT Class 9 Math Chapter 13 Notes, along with a detailed explanation. The surface area of any three-dimensional object can be divided into three categories: Curved Surface Area (CSA), Lateral Surface Area (LSA), and Total Surface Area (TSA). CBSE class 9 Math chapter 13 notes will offer students an overview of all the significant and relevant sections as well as highlight the significant references from the CBSE revision notes. The latest NCERT Syllabus and CBSE regulations were used to build, notes for class 9 Math chapter 13. For more information on any of the topics presented in this chapter, students can refer to the following resources.

Also, students can refer,

NCERT Class 9 Math Chapter 13 Notes: Topic 1

Area, Surface, And Volume

The quantity of space inside a 2D object's boundary is referred to as its area. The overall area occupied by a surface of a solid 3D object is measured by its surface area. It is measured in m2, cm2 etc. The quantity of 3D space encompassed by a closed border is referred to as volume. It is measured in m3, cm3, litre etc. It is commonly used to calculate the amount of liquid, air, grains, and other materials in a three-dimensional container.

NCERT Class 9 Math Chapter 13 Notes: Topic 2


A cuboid is a figure that is surrounded by six rectangular surfaces. A cuboid's opposite surface is equal and parallel. There are 12 edges and 8 corners on a cuboid. The vertex of a cuboid is each of its four corners. The diagonal of a cuboid is the line segment connecting the opposite vertices. In a cuboid, there are four diagonals.


Volume of cuboid = Length × Breadth × Height = lbh
Lateral surface area = 2 (Length + Breadth) × Height = 2 (l + b) h
Total surface area = 2 (Length × Breadth + Breadth × Height + Height × Length) = 2 (lb+bh+hl)
Total length of cuboid = 4 (l + b + h)

Diagonal of cuboid = √ [(l)2+(b)2+(h)2]

NCERT Class 9 Math Chapter 13 Notes: Topic 3


A cube is a cuboid with the same length, width, and height. Six surfaces, twelve edges, eight corners, and four diagonals make up a cube.


Volume of cube= (lenghth of side)3 = l3
Lateral surface area = 4 × (lenghth of side)2 = 4 l2
Total surface area = 6 × (lenghth of side)2 = 6 l2
Total length of cube = 12 l
Diagonal of cube = √3 l

NCERT Class 9 Math Chapter 13 Notes: Topic 4

Right Circular Cylinder

A solid generated by the revolution of a rectangle around one of its sides is known as a right circular cylinder.


The volume of a cylinder = πr2h
Curved surface area or lateral surface area = 2πrh
Total surface area = Curved surface + 2 × Base area = 2πrh + 2πr2 = 2πr(h+r)

NCERT Class 9 Math Chapter 13 Notes: Topic 5


A right circular cone is a solid formed when a triangle is rotated around one of its sides (other than hypotenuse).


Volume of cone = (1/3)πr2h

Curved surface area or lateral surface area = πrl

Total surface area = Curved surface area + Base area

= πrl + πr2


l = √ (h2+r2)

h = √ (l2-r2)

r = √ (l2-h2)

NCERT Class 9 Math Chapter 13 Notes: Topic 6


A solid encircled by a curving surface whose points are all the same distance apart from a fixed point. The fixed point is known as the sphere's centre. The radius of the sphere is the line segment connecting the sphere's centre to any point on the surface.


Volume of the sphere = (4/3)πr3

Surface area of the sphere = 4πr2

NCERT Class 9 Math Chapter 13 Notes: Topic 7


A plane that passes through the centre of a sphere divides it into two equal halves. Each component is referred to as a hemisphere.


Volume of hemisphere = (2/3)πr3
The curved surface area of hemisphere = 2πr2
Total surface area of hemisphere = 2πr2 + πr2 = 3πr2

Significance of NCERT Class 9 Math Chapter 13 Notes

Surface area and volumes class 9 notes are based on the current CBSE syllabus and provide an outline of the class 9 chapter Surface area and volumes. The purpose of CBSE class 9 Math chapter 13 notes is to help students learn and revise more easily. Students will learn about the surface areas and volumes of various forms such as the cuboid, cube, right circular cylinder, right circular cone, and sphere through NCERT notes for class 9 chapter. class 9 Surface Areas and Volumes notes present the most important notes and formulas for each of the shapes in a simple manner. of NCERT Class 9 Math Chapter 13 Notes help students to recollect the points easily and crack good scores in exams. Students can download Surface Areas and Volumes class 11 pdf download and study offline.

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NCERT Class 9 Notes Chapter wise

Frequently Asked Question (FAQs)

1. What is mean by volume of a shape?

NCERT Class 9 Math Chapter 13 Notes provide a definition for volume. The volume of any 3-D object is the amount of space it takes up. Because the volume of a solid object is the product of three dimensions, we use cubic units to express it.

2. What are the peculiarities of a cuboid?

Six rectangular faces are arranged at right angles to form the cuboid. The sum of the areas of a cuboid's six rectangular sides give its entire surface area.

3. What is meant by lateral surface area?

The area of all sides except the top and bottom faces is known as lateral surface area (LSA).

4. What is right angles cylinder?

A cylinder is formed when a rectangular sheet is folded with one side as the axis. It is the cylinder's curved surface. A right circular cylinder is formed when this curved surface is covered by two parallel circular bases.

5. What is the definition of a sphere? Give some examples

The sphere is a three-dimensional solid made up of all the points in space that are separated by a constant distance, called the radius, from a fixed point, called the centre. Examples include cricket balls, planets, the moon etc.


Get answers from students and experts

A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg


An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)


Option 2)

\; K\;

Option 3)


Option 4)


In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)


Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)


Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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