Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > Important Formulas: Surface Areas & Volumes
Important Formulas: Surface Areas & Volumes | Mathematics (Maths) Class 9 PDF Download
Definitions
- Surface area is like the total paper to cover a 3D object.
- Volume is the space it occupies.
- Cuboid: A 3D box-shaped object with 6 rectangular faces (e.g., bricks, books). Has different lengths, breadths, and heights.
- Cube: A special cuboid where all edges are equal in length. All 6 faces are equal squares (e.g., dice, Rubik’s cube).
- Cylinder: A solid with two parallel circular bases and one curved surface (e.g., cans, pipes).
- Hollow Cylinder: A cylindrical pipe with an empty interior. It has both an inner radius and an outer radius. Example: water pipes or straws.
- Right Circular Cones: These cones are three-dimensional shapes with a circular base that narrows down to a single point known as the apex or vertex. For example, an ice cream cone.
- Total Surface Area of a Cone: The total surface area of a cone is the total of its curved surface area (CSA) and the area of its base.
- Spheres: These are completely round three-dimensional shapes, similar to balls or globes. Every point on a sphere's surface is the same distance from its centre.
- Hemispheres: A hemisphere is half of a sphere ('hemi' means half).
- Hollow Sphere (Spherical Shell): A 3D shell with both an outer and inner radius. It’s like a ball with a hollow inside (e.g., a cricket ball or a basketball).
Formulas
- Total surface area of a cuboid = 2[ℓb + bh + ℓh]
- Total surface area of a cube = 6(side)2
- Lateral surface area of a cuboid = Area of walls of a room = 2(ℓ + b) x h
- Lateral surface area of a cube = 4a2
- Curved surface area of cylinder = 2πrh
- Total surface area of a cylinder = 2πr(r + h)
- Curved surface area of a cone = πrℓ
- Total surface area of a cone = πr(r + ℓ)
- Surface area of a sphere = 4πr2
- Curved surface area of a hemisphere = 2πr2
- Total surface area of a hemisphere = 3πr2
- Volume of a cuboid = ℓ x b x h
- Volume of a cube = (side)3
- Volume of a cylinder = πr2h
- Volume of a cone =
- Volume of a hemisphere =
. - Volume of a sphere =
- 1000 cm3 = 1 litre
Now, here is the table for all the formulas in a summarised manner-
The document Important Formulas: Surface Areas & Volumes | Mathematics (Maths) Class 9 is a part of the Class 9 Course Mathematics (Maths) Class 9.
All you need of Class 9 at this link: Class 9
|
40 videos|560 docs|57 tests
|
FAQs on Important Formulas: Surface Areas & Volumes - Mathematics (Maths) Class 9
| 1. What are the basic formulas for calculating the surface area of common geometric shapes? |  |
Ans. The basic formulas for calculating the surface area of common geometric shapes are as follows:
- Cube: \(6a^2\), where \(a\) is the length of a side.
- Rectangular Prism: \(2(lw + lh + wh)\), where \(l\), \(w\), and \(h\) are the length, width, and height, respectively.
- Sphere: \(4\pi r^2\), where \(r\) is the radius.
- Cylinder: \(2\pi r(h + r)\), where \(r\) is the radius and \(h\) is the height.
- Cone: \(\pi r(r + l)\), where \(r\) is the radius and \(l\) is the slant height.
| 2. How can I calculate the volume of a cylinder? | |
Ans. The volume of a cylinder can be calculated using the formula \(V = \pi r^2 h\), where \(r\) is the radius of the base and \(h\) is the height of the cylinder.
| 3. What is the formula for the volume of a sphere, and how is it derived? | |
Ans. The formula for the volume of a sphere is \(V = \frac{4}{3}\pi r^3\), where \(r\) is the radius. It is derived using calculus by integrating the area of circular cross-sections of the sphere.
| 4. How do I find the surface area of a cone? | |
Ans. The surface area of a cone can be calculated using the formula \(S = \pi r(l + r)\), where \(r\) is the radius of the base and \(l\) is the slant height. The formula includes the area of the base (\(\pi r^2\)) and the lateral area (\(\pi rl\)).
| 5. What is the difference between surface area and volume? | |
Ans. Surface area refers to the total area that the surface of a three-dimensional object occupies, measured in square units, while volume measures the amount of space an object occupies, measured in cubic units. Surface area is concerned with the exterior of the shape, whereas volume deals with the capacity within the shape.
About this Document
10.6K Views
4.70/5
Rating
Sep 07, 2025
Last updated
Related Exams
Document Description: Important Formulas: Surface Areas & Volumes for Class 9 2025 is part of Mathematics (Maths) Class 9 preparation.
The notes and questions for Important Formulas: Surface Areas & Volumes have been prepared according to the Class 9 exam syllabus. Information about Important Formulas: Surface Areas & Volumes covers topics
like Definitions, Formulas and Important Formulas: Surface Areas & Volumes Example, for Class 9 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Important Formulas: Surface Areas & Volumes.
Introduction of Important Formulas: Surface Areas & Volumes in English is available as part of our Mathematics (Maths) Class 9
for Class 9 & Important Formulas: Surface Areas & Volumes in Hindi for Mathematics (Maths) Class 9 course.
Download more important topics related with notes, lectures and mock test series for Class 9
Exam by signing up for free. Class 9: Important Formulas: Surface Areas & Volumes | Mathematics (Maths) Class 9
Description
Full syllabus notes, lecture & questions for Important Formulas: Surface Areas & Volumes | Mathematics (Maths) Class 9 - Class 9 | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 9 | Best notes, free PDF download
Information about Important Formulas: Surface Areas & Volumes
In this doc you can find the meaning of Important Formulas: Surface Areas & Volumes defined & explained in the simplest way possible. Besides explaining types of
Important Formulas: Surface Areas & Volumes theory, EduRev gives you an ample number of questions to practice Important Formulas: Surface Areas & Volumes tests, examples and also practice Class 9
tests
Related Searches
study material
,Extra Questions
,Free
,Important Formulas: Surface Areas & Volumes | Mathematics (Maths) Class 9
,Sample Paper
,practice quizzes
,Viva Questions
,Previous Year Questions with Solutions
,Important questions
,video lectures
,mock tests for examination
,Objective type Questions
,shortcuts and tricks
,ppt
,Semester Notes
,Exam
,Important Formulas: Surface Areas & Volumes | Mathematics (Maths) Class 9
,Summary
,MCQs
,Important Formulas: Surface Areas & Volumes | Mathematics (Maths) Class 9
,past year papers
;
Additional Information about Important Formulas: Surface Areas & Volumes for Class 9 Preparation
Important Formulas: Surface Areas & Volumes Free PDF Download
The Important Formulas: Surface Areas & Volumes is an invaluable resource that delves deep into the core of the Class 9 exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the Important Formulas: Surface Areas & Volumes now and kickstart your journey towards success in the Class 9 exam.
Importance of Important Formulas: Surface Areas & Volumes
The importance of Important Formulas: Surface Areas & Volumes cannot be overstated, especially for Class 9 aspirants.
This document holds the key to success in the Class 9 exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
Important Formulas: Surface Areas & Volumes Notes
Important Formulas: Surface Areas & Volumes Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to Important Formulas: Surface Areas & Volumes.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, Important Formulas: Surface Areas & Volumes Notes on EduRev are your ultimate resource for success.
Important Formulas: Surface Areas & Volumes Class 9 Questions
The "Important Formulas: Surface Areas & Volumes Class 9 Questions" guide is a valuable resource for all aspiring students preparing for the
Class 9 exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study Important Formulas: Surface Areas & Volumes on the App
Students of Class 9 can study Important Formulas: Surface Areas & Volumes alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Important Formulas: Surface Areas & Volumes,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Important Formulas: Surface Areas & Volumes is prepared as per the latest Class 9 syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup