📝 Chapter Notes & Revision

Surface Areas and Volumes

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Quick Revision Notes & Formula Sheet

Class 9 Mathematics

Chapter: Surface Areas and Volumes

Introduction

In this chapter, we deal with 3D (three-dimensional) shapes. Unlike 2D shapes (which have area and perimeter), 3D shapes occupy space and have Total Surface Area (TSA), Curved/Lateral Surface Area (CSA/LSA), and Volume (V).

1. Cuboid (घناभ)

A cuboid is a 3D box bounded by six rectangular plane faces.

  • Let length = $l$, breadth = $b$, and height = $h$.

  • Total Surface Area (TSA) = $2(lb + bh + hl)$

  • Lateral Surface Area (LSA) / Area of 4 walls = $2(l + b)h$

  • Volume (V) = $l \times b \times h$

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

2. Cube (घन)

A cube is a special cuboid where length, breadth, and height are equal ($l = b = h = a$).

  • Let the side of the cube = $a$.

  • Total Surface Area (TSA) = $6a^2$

  • Lateral Surface Area (LSA) = $4a^2$

  • Volume (V) = $a^3$

  • Length of Diagonal = $\sqrt{3}a$

3. Right Circular Cylinder (लंबवृत्त बेलन)

A cylinder is shaped like a solid circular pipe or a can.

  • Let radius of the base = $r$, and height = $h$.

  • Curved Surface Area (CSA) = $2\pi rh$

  • Total Surface Area (TSA) = $2\pi r(r + h)$ (CSA + Area of 2 circular bases)

  • Volume (V) = $\pi r^2 h$

4. Right Circular Cone (लंबवृत्त शंकु)

A cone is shaped like a birthday cap or an ice-cream cone.

  • Let radius = $r$, height = $h$, and slant height = $l$.

  • Slant Height ($l$) = $\sqrt{r^2 + h^2}$

  • Curved Surface Area (CSA) = $\pi rl$

  • Total Surface Area (TSA) = $\pi r(l + r)$ (CSA + Area of circular base)

  • Volume (V) = $\frac{1}{3}\pi r^2 h$

5. Sphere (गोोला)

A sphere is a perfectly round 3D geometrical object, like a ball.

  • Let radius = $r$.

  • Surface Area (SA) = $4\pi r^2$

  • Volume (V) = $\frac{4}{3}\pi r^3$

6. Hemisphere (अर्धगोोला)

A hemisphere is half of a sphere divided along a plane passing through its center.

  • Let radius = $r$.

  • Curved Surface Area (CSA) = $2\pi r^2$

  • Total Surface Area (TSA) = $3\pi r^2$ (CSA + Area of top circular face)

  • Volume (V) = $\frac{2}{3}\pi r^3$

Important Conversion Units

  • $1 \text{ Litre} = 1000 \text{ cm}^3$
  • $1 \text{ m}^3 = 1000 \text{ Litres}$
  • $1 \text{ m} = 100 \text{ cm}$
  • $1 \text{ m}^2 = 10,000 \text{ cm}^2$

Note: Unless stated otherwise, take $\pi = \frac{22}{7}$ or $3.14$.