Tube (Hollow Cylinder) Formulas
A tube is a cylinder with a cylindrical hole through the middle.
Volume:
$V = πh(R² - r²)$
Lateral Surface Area:
$LSA = 2π(R + r)h$
Top & Bottom Area:
$TBA = 2π(R² - r²)$
Total Surface Area:
$TSA = 2π(R + r)h + 2π(R² - r²)$
Where $R$ is the outer radius, $r$ is the inner radius, and $h$ is the height.
Example:
For a tube with outer radius 5, inner radius 3, and height 8 units:
- Volume = π × 8 × (5² - 3²) = π × 8 × 16 = 128π ≈ 402.12 cubic units
- Lateral Area = 2π(5 + 3) × 8 = 128π ≈ 402.12 square units
- Top & Bottom = 2π(25 - 9) = 32π ≈ 100.53 square units
- Total Surface Area = 128π + 32π = 160π ≈ 502.65 square units