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CBSE Notes
Class 9
Maths
Chapter 11 Surface Areas and Volumes

CBSE Notes For Class 9 Maths Chapter 11 Surface Areas and Volumes

1.0Introduction to Surface Areas and Volumes

We often encounter a variety of three-dimensional objects in our day-to-day life such as boxes, spheres, cylinders, and cones that take up space and have surfaces that can be measured. In maths, we measure these quantities and apply them in daily applications, such as when measuring milk or buying wood by surface areas. 

2.0Download CBSE Notes for Class 9 Maths Chapter 11 Surface Areas and Volumes - Free PDF

Students can now download free PDF notes for CBSE Class 9 Maths Chapter 11 – Surface Areas and Volumes, designed to simplify 3D geometry concepts and improve understanding.

Class 9 Maths Chapter 11 Revision Notes:

3.0CBSE Class 9 Maths Chapter-11 Surface Areas and Volumes - Revision Notes

What is Surface Area and Volume?

  • Surface area measures the total area that the surface of an object covers. It is the sum of the areas of all the outer faces.  
  • The curved Surface area measures only the outer sides or curved side of an object but not the base.
  • Volume measures the space that an object occupies. It also refers to the capacity of a 3D object. 

There are different objects, and we have different formulas for each object. 

  1. Cone 

A cone is a 3-dimensional geometric shape with a circular base and one curved surface connecting the base to a point, called an apex or vertex, above the base. The tip of “h” in the figure.

Formula related to Cone

Formula for a cone

h = height of cone

L = Slant height of cone

r = Radius of cone 

Slant height 

L2 = h2 + r2

Curved surface area of cone =πrL

The total surface area of the cone =πr(L+r)

The volume of the cone =31​πr2h

  1. Hemisphere 

A hemisphere is a three-dimensional figure composed of a sphere cut into two halves. Then, it will have one curved surface, namely the outer part of the sphere, and one flat circular base representing half of the volume and surface area of the sphere.

Formulas related to Hemisphere

Formula of a hemisphere

The curved surface area of the hemisphere =2πr2

The Total surface area of the hemisphere =3πr2

The Volume of the hemisphere =32​πr3

  1. Sphere 

In maths, a sphere is three-dimensional and is a perfectly round shape. Every point on its surface is equidistant from the centre. It has no edges or corners, merely a smooth, curved surface. This is the reason it does not have a curved surface area.

Formulas related to Sphere 

Formula of a sphere

The Total surface area of the sphere =4πr2

The Volume of the sphere =34​πr3

4.0How do you solve questions related to Surface areas and Volumes?

Question 1: Find the total surface area, volume, and curved surface area of an inverted hat that is in the shape of a cone, given that its height is 28 cm and radius is 14cm. 

Solution: h = 28, r = 14, L = ? 

L2 = 282 + 142

L2 = 784 + 196

L2 = 980

L = 31.31cm

Sample questions on cone

Total Surface area of cone =πr(l+r)=722​×14×(31.31+14) = 1994cm2

Curved Surface area of cone =πrl

722​×14×31.31

=1378 cm2

The volume of the cone =31​πr2 h

31​×722​×14×14×28

=5749 cm3

Question 2: Find the volume of a sphere whose surface area is 132cm2. 

Solution: Surface area of a sphere =132=4πr2

4×722​×r2=154

r2=4×22154×7​

r=7/2

The volume of the sphere =34​πr3

=34​×722​×2×2×27×7×7​=179.67 cm3

Question 3: Find the total surface area of the hemisphere, which has a radius of 7cm. 

Answer: Total surface area of hemisphere =3πr2

=3×722​×7×7

=464 cm2

5.0Key Features of CBSE Maths Notes for Class 9 Chapter 11

  • The notes are aligned with the latest CBSE curriculum. 
  • These CBSE Notes provide the solved problems to get a better understanding of surface areas and volumes.
  • Visual aid is provided to help you understand the figures more clearly. 
  • The notes are well-edited and analysed to ensure 100% accuracy.

Chapter-wise CBSE Notes for Class 9 Maths:

Class 9 Maths Chapter 1 - Number Systems Notes

Class 9 Maths Chapter 2 - Polynomial Notes

Class 9 Maths Chapter 3 - Coordinate Geometry Notes

Class 9 Maths Chapter 4 - Linear Equation In Two Variables Notes

Class 9 Maths Chapter 5 - Introduction To Euclids Geometry Notes

Class 9 Maths Chapter 6 - Lines and Angles Notes

Class 9 Maths Chapter 7 - Triangles Notes

Class 9 Maths Chapter 8 - Quadrilaterals Notes

Class 9 Maths Chapter 9 - Circles Notes

Class 9 Maths Chapter 10 - Herons Formula Notes

Class 9 Maths Chapter 11 - Surface Areas and Volumes Notes

Class 9 Maths Chapter 12 - Statistics Notes


Chapter-wise NCERT Solutions for Class 9 Maths:

Chapter 1: Number Systems

Chapter 2: Polynomials

Chapter 3: Coordinate Geometry

Chapter 4: Linear Equations in Two Variables

Chapter 5: Introduction to Euclid’s Geometry

Chapter 6: Lines and Angles

Chapter 7: Triangles

Chapter 8: Quadrilaterals

Chapter 9: Circles

Chapter 10: Heron’s Formula

Chapter 11: Surface Areas and Volumes

Chapter 12: Statistics


Frequently Asked Questions

For irregular objects, surface area and volume are usually approximated by subdivision into simpler shapes. Alternatively, various other methods, such as water displacement or 3D scanning, can be applied for accurate calculations.

In maths, surface area and volume measure different properties, so they simply can't be the same. Surface area measures the outer covering of an object, while volume measures the space it occupies.

To visualise volume, imagine filling the container with water, and for the surface area, imagine wrapping the container with paper.

Calculating the surface area of these objects can help in coating, wrapping these objects, manufacturing buildings, etc.

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