Surface Areas and Volumes

• Introduction
  • Dimensions: 2D (Area) to 3D (Solid Shapes)
  • Surface Area: Total area covered by the surface of a 3D object
  • Volume: Amount of space occupied by a 3D object
• Cuboid and Cube
  • Cuboid
    • Total Surface Area (TSA) = $2(lb + bh + hl)$
    • Curved/Lateral Surface Area (LSA) = $2(l + b)h$
    • Volume ($V$) = $l \times b \times h$
    • Diagonal = $\sqrt{l^2 + b^2 + h^2}$
  • Cube
    • Total Surface Area (TSA) = $6a^2$
    • Lateral Surface Area (LSA) = $4a^2$
    • Volume ($V$) = $a^3$
• Right Circular Cylinder
  • Curved Surface Area (CSA) = $2\pi rh$
  • Total Surface Area (TSA) = $2\pi r(r + h)$
  • Volume ($V$) = $\pi r^2 h$
  • Key Components: Radius ($r$), Height ($h$)
• Right Circular Cone
  • Slant Height ($l$) = $\sqrt{r^2 + h^2}$
  • Curved Surface Area (CSA) = $\pi rl$
  • Total Surface Area (TSA) = $\pi r(l + r)$
  • Volume ($V$) = $\frac{1}{3}\pi r^2 h$
• Sphere and Hemisphere
  • Sphere
    • Surface Area = $4\pi r^2$
    • Volume ($V$) = $\frac{4}{3}\pi r^3$
  • Hemisphere
    • Curved Surface Area (CSA) = $2\pi r^2$
    • Total Surface Area (TSA) = $3\pi r^2$
    • Volume ($V$) = $\frac{2}{3}\pi r^3$
• Important Units and Conversions
  • Length: $1 \text{ m} = 100 \text{ cm}$
  • Area: $1 \text{ m}^2 = 10,000 \text{ cm}^2$
  • Volume & Capacity: $1 \text{ m}^3 = 1000 \text{ liters}$
  • Capacity: $1 \text{ liter} = 1000 \text{ cm}^3$
• Problem-Solving Applications
  • Conversion of solid from one shape to another (Volume remains constant)
  • Combined solid figures (Sum of CSAs/TSAs or Volumes)