# Surface Areas and Volumes class 9 Notes Mathematics

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## 9 Mathematics notes Chapter 13 Surface Areas and Volumes

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