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.
2.0CBSE 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.
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

h = height of cone
L = Slant height of cone
r = Radius of cone
Slant height
L2 = h2 + r2
Curved surface area of cone
The total surface area of the cone
The volume of the cone
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

The curved surface area of the hemisphere
The Total surface area of the hemisphere
The Volume of the hemisphere
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

The Total surface area of the sphere
The Volume of the sphere
3.0How 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

Total Surface area of cone = 1994cm2
Curved Surface area of cone
The volume of the cone
Question 2: Find the volume of a sphere whose surface area is 132cm2.
Solution: Surface area of a sphere
The volume of the sphere
Question 3: Find the total surface area of the hemisphere, which has a radius of 7cm.
Answer: Total surface area of hemisphere
4.0Key Features of CBSE Maths Notes for Class 9 Chapter 11
- The notes are aligned with the latest CBSE curriculum.
- These 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.
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