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Revision Notes for Class 9 Mathematics Chapter 13 Surface areas and Volumes
Class 9 Mathematics students should refer to the following concepts and notes for Chapter 13 Surface areas and Volumes in Class 9. These exam notes for Class 9 Mathematics will be very useful for upcoming class tests and examinations and help you to score good marks
Chapter 13 Surface areas and Volumes Notes Class 9 Mathematics
CBSE Class 9 Concepts for Surface Areas and Volumes. Learning the important concepts is very important for every student to get better marks in examinations. The concepts should be clear which will help in faster learning. The attached concepts made as per NCERT and CBSE pattern will help the student to understand the chapter and score better marks in the examinations.
Chapter 13
Surface Areas and Volumes
Chapter Notes
Top Definitions
1. A Cube is a special type of cuboids in which length = breadth = height. Also called an edge of a cube.
2. A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball.
3. A cylinder is a solid or a hollow object that has a circular base and a circular top of the same size.
4. A hemisphere is half of a sphere.
5. If a right circular is cut off by a plane parallel to its base, then the portion of the cone between the plane and the base of the cone is called a frustum of the cone.
Top Concepts
1. The total surface area of the solid formed by the combination of solids is the sum of the curved surface area of each of the individual parts.
2. A solid is melted and converted to another, volume of both the solids remains the same, assuming there is no wastage in the conversions. The surface area of the two solids may or may not be the same.
3. A frustum can be obtained by cutting a cone by a plane, parallel to the base of the cone.
4. The solids having the same curved surface do not necessarily occupy the same volume.
Top Formulae
1. Cuboids:
Lateral surface area Or Area of four walls = 2(ℓ + b) h
Total surface area = 2(ℓb + bh + hℓ)
Volume = ℓ x b x h
Diagonal of a cuboids = √l2 + b2 + h2
2. Cube Lateral surface area Or Area of four walls = 4 x (edge)2 Total surface area = 6 x (edge)² Volume = (edge)3 Diagonal of a cube = 3 x edge.
3. Right circular cylinder: Area of each end or Base area = pr² Area of curved surface or lateral surface area = perimeter of the base x height = 2p r h
Total surface area (including both ends) = 2 prh + 2pr² = 2pr (h + r) Volume = (Area of the base0 x height = pr²h
4. Right circular hollow cylinder: Area of curved surface
= (External surface) + (Internal surface)
= (2pRh + 2prh) = 2 (pR² - pr²)
= [2ph(R+ r) + 2p (R² - r²)]
= [2p(R + r) (h + R – r)]
Volume of the material
= (External volume) – (Internal volume)
= (pR²h - pr²h) = ph (R² - r²)
5. Right circular cone:
Slant height (ℓ) = √h2 + r2
Area of curved surface = prℓ = pr √h2 + r2
Total surface area = Area of curved surface + Area of base = prℓ + pr² = pr (ℓ + r) Volume = 1/3pr2
6. Sphere:
Surface area = 4 pr²
Volume = 4/3pr3
7. Spherical shell:
Surface area (outer) = 4pR²
Volume of material =4/3 pr³ - 4/3 pr³= 4/3p (R³ - r³)
8. Hemisphere:
Area of curved surface = 2 pr²
Total surface Area = Area of curved surface + Area of base
= 2 pr² + pr²
= 3pr²
Volume = 2/3(pr3)
9. Frustum of a cone:
Total surface area = p[R² + r² + ℓ (R + r)]
Volume of the material =1/3ph (R² + r² + Rr)
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CBSE Class 9 Mathematics Chapter 13 Surface areas and Volumes Notes
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Notes for Mathematics CBSE Class 9 Chapter 13 Surface areas and Volumes
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Chapter 13 Surface areas and Volumes Notes for Mathematics CBSE Class 9
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Chapter 13 Surface areas and Volumes CBSE Class 9 Mathematics Notes
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Notes for CBSE Mathematics Class 9 Chapter 13 Surface areas and Volumes
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