The volume of a cylinder is calculated using this simple formula:
V = π × r² × h
Where:
The most common units are:
Example calculations of cylinder volume
Example 1 – Basic (small cylinder)
Radius = 5 cm
Height = 12 cm
V = π × r² × h
V = π × 5² × 12
V = π × 25 × 12
V = π × 300
V ≈ 3.14159 × 300
V ≈ 942.48 cm³
Example 2 – Medium cylinder (using 3.14 for π)
Diameter = 20 cm → radius = 10 cm
Height = 35 cm
V = π × r² × h
V = 3.14 × 10² × 35
V = 3.14 × 100 × 35
V = 3.14 × 3500
V = 10,990 cm³
(or 10.99 liters)
Example 3 – Large cylinder (real-world tank example)
Radius = 1.2 meters
Height = 4.5 meters
V = π × r² × h
V = π × (1.2)² × 4.5
V = π × 1.44 × 4.5
V = π × 6.48
V ≈ 3.14159 × 6.48
V ≈ 20.36 m³
The surface area of a cylinder measures the total area covering its outer surface. For a right circular cylinder (the most common type), there are two main types:
Formulas
Curved / Lateral Surface Area (CSA or LSA)
CSA = 2πrh
(or sometimes written as πdh, since d = 2r)
Total Surface Area (TSA)
TSA = 2πr² + 2πrh
= 2πr(r + h) ← most convenient form to remember/use
Where:
Example 1 – Basic (small can)
Radius r = 4 cm
Height h = 10 cm
Curved surface area = 2πrh = 2 × π × 4 × 10 = 80π ≈ 251.33 cm²
Total surface area = 2πr(r + h) = 2π × 4 × (4 + 10) = 8π × 14 = 112π ≈ 351.86 cm²
Example 2 – Medium (paint can, using π ≈ 3.14)
Radius r = 7.5 cm
Height h = 12 cm
Curved = 2 × 3.14 × 7.5 × 12 = 565.2 cm²
Total = 2 × 3.14 × 7.5 × (7.5 + 12) = 15 × 3.14 × 19.5 ≈ 919.95 cm²
Example 3 – Large (storage tank)
Radius r = 2.5 m
Height h = 8 m
Curved = 2π × 2.5 × 8 = 40π ≈ 125.66 m²
Total = 2π × 2.5 × (2.5 + 8) = 5π × 10.5 = 52.5π ≈ 164.93 m²
The volume of a hollow cylinder (also called a cylindrical shell, tube, or pipe) is the space between an outer cylinder and a smaller inner cylinder sharing the same height and central axis.
Formula
V = π (R² - r²) h
(or equivalently V = π (R² - r²) h cubic units)
Where:
R = outer radius
r = inner radius (r < R)
h = height (same for both inner and outer parts)
π ≈ 3.14159
This comes from subtracting the volume of the inner solid cylinder from the outer one:
V = (π R² h) - (π r² h) = π h (R² - r²)
Example 1 – Basic pipe
Outer radius R = 6 cm
Inner radius r = 4 cm
Height h = 10 cm
V = π (6² - 4²) × 10
V = π (36 - 16) × 10
V = π × 20 × 10
V = 200π
V ≈ 628.32 cm³
Example 2 – Metal tube (using π ≈ 3.14)
Outer radius R = 5 cm
Inner radius r = 3.5 cm
Height h = 25 cm
V = 3.14 × (25 - 12.25) × 25
V = 3.14 × 12.75 × 25
V = 3.14 × 318.75
V ≈ 1,000.875 cm³ (about 1 liter)
Example 3 – Large hollow column
Outer radius R = 1.5 m
Inner radius r = 1.2 m
Height h = 6 m
V = π (2.25 - 1.44) × 6
V = π × 0.81 × 6
V = π × 4.86
V ≈ 15.27 m³
An oblique cylinder (slanted cylinder) has circular bases that are parallel, but the side is not perpendicular to the bases (unlike a right cylinder).
Key fact: The volume is exactly the same as a right circular cylinder with the same base radius and perpendicular height.
Formula
V = π r² h
Where:
The slant does not affect the volume because you can think of the cylinder as stacked thin disks; sliding them sideways (making it oblique) keeps the total volume unchanged.
Oblique cylinder calculation
Radius r = 5 cm
Perpendicular height h = 12 cm (measured straight up/down between bases, even if slanted) V = π × 5² × 12
V = π × 25 × 12
V = 300π
V ≈ 942.48 cm³ (This is identical to the volume of a right cylinder with r = 5 cm and h = 12 cm.)