# Surface Areas and Volumes class 9 Notes Mathematics

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## CBSE Guide Surface Areas and Volumes class 9 Notes

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## 9 Mathematics notes Chapter 13 Surface Areas and Volumes

Download CBSE class 9th revision notes for Chapter 13 Surface Areas and Volumes in PDF format for free. Download revision notes for Surface Areas and Volumes class 9 Notes and score high in exams. These are the Surface Areas and Volumes class 9 Notes prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the best tips recommended by teachers during exam days.

CBSE Class 09 Mathematics
Revison Notes
CHAPTER 13
SURFACE AREAS AND VOLUMES

1. Surface Area of a Cuboid and a Cube
2. Surface Area of a Right Circular Cylinder
3. Surface Area of a Right Circular Cone
4. Surface Area of a Sphere
5. Volume of a Cuboid
6. Volume of a Cylinder
7. Volume of a Right Circular Cone
8. Volume of a Sphere

Cuboid – with length $l$, breadth $b$ and height $h$

Perimeter of Cuboid = $4\left( {l + b + h} \right)$

Length of diagonal = $\sqrt {{l^2} + {b^2} + {h^2}}$

Lateral surface area = $2h\left( {l + b} \right)$

Total surface area = $2\left( {lb + bh + hl} \right)$

Volume = $lbh$

Cube – with side $a$

Perimeter of cube = 12 x edge

Lateral surface area = $4{a^2}$

Total surface area = $6{a^2}$

Volume = ${a^3}$

Right Prism

Lateral Surface area = Perimeter of base x Height

Total surface area = Lateral Surface area + 2(Area of one end)

Volume = Area of base x Height

Right Circular Cylinder – with radius $r$ and height $h$

Curved Surface area = $2\pi rh$

Total surface area = $2\pi r\left( {r + h} \right)$

Volume = $\pi {r^2}h$

Hollow Cylinder

Each base surface area = $\pi \left( {{{\rm{R}}^2} - {r^2}} \right)$

Curved surface area = $2\pi h\left( {{\rm{R}} + r} \right)$

Total surface area = $2\pi \left( {{\rm{R}} + r} \right)\left( {h + {\rm{R}} - r} \right)$

Volume = $\pi h\left( {{{\rm{R}}^2} - {r^2}} \right)$

Right Pyramid

Lateral Surface area = ${1 \over 2}$ x Perimeter of base x Slant Height

Total surface area = Lateral Surface area + Area of base

Volume = ${1 \over 3}$ x Area of base x Height

Right Circular Cone – with with radius $r$, height $h$ and slant height $l$

A right circular cone is a solid generated by revolving a line segment which passes through a fixed point and which makes a constant angle with a fixed line. The fixed point is called the vertex of the cone, the fixed line is called the axis of the cone.

Curved Surface area = $\pi rl$

Total surface area = $\pi r\left( {l + r} \right)$

Volume = ${1 \over 3}$$\pi {r^2}h$

Volume = ${1 \over 3}$ x Area of the base x height

Sphere (Solid) – with radius $r$

The set of all points in space which are equidistant from a fixed point is called a sphere. The fixed point is called the centre of the sphere and the constant distance is called its radius.

Curved Surface Area = $4\pi {r^2}$

Total surface area = $4\pi {r^2}$

Volume = ${4 \over 3}\pi {r^3}$

Hemisphere – with radius $r$

Curved Surface Area = $2\pi {r^2}$

Total surface area = $3\pi {r^2}$

Volume = ${2 \over 3}\pi {r^3}$

Spherical shell – with inner with radius $r$ and outer radius R

Volume = ${4 \over 3}\pi \left( {{{\rm{R}}^3} - {r^3}} \right)$

## Surface Areas and Volumes class 9 Notes

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## CBSE Class-9 Revision Notes and Key Points

Surface Areas and Volumes class 9 Notes. CBSE quick revision note for Class-9 Mathematics, Chemistry, Maths, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

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