Understanding Volume of a Cylinder Calculator
A cylinder is a 3D geometric shape with two identical circular bases connected by a curved lateral surface. Common real-world examples include cans, pipes, tubes, tanks, and columns.
Volume V = π × r² × h
Lateral (Curved) Surface Area = 2 × π × r × h
Total Surface Area = 2πr² + 2πrh = 2πr(r + h)
Diameter d = 2r
Worked Examples
Example 1: Water Pipe
A cylindrical pipe has radius 0.05 m and length 10 m. Find its volume (capacity).
V = π × 0.05² × 10 = π × 0.0025 × 10 ≈ 0.0785 m³ = 78.5 litres
Example 2: Cylindrical Can
A can has diameter 7 cm and height 12 cm. Find volume and surface area.
r = 7/2 = 3.5 cm
V = π × 3.5² × 12 = π × 12.25 × 12 ≈ 461.81 cm³
Total SA = 2π × 3.5 × (3.5 + 12) = 2π × 3.5 × 15.5 ≈ 340.59 cm²
V = π × 3.5² × 12 = π × 12.25 × 12 ≈ 461.81 cm³
Total SA = 2π × 3.5 × (3.5 + 12) = 2π × 3.5 × 15.5 ≈ 340.59 cm²
Example 3: Storage Tank
A cylindrical tank has radius 2 m and height 5 m. How many litres can it hold?
V = π × 4 × 5 = 20π ≈ 62.83 m³ = 62,832 litres
Cylinder Formulas Comparison Table
| Measurement | Formula | r=3, h=8 result |
|---|---|---|
| Volume | πr²h | 226.19 cubic units |
| Lateral Surface Area | 2πrh | 150.80 sq units |
| Base Area (one circle) | πr² | 28.27 sq units |
| Total Surface Area | 2πr(r+h) | 207.35 sq units |
Real-World Uses
- Engineering: Tank capacity, pipe flow rates, boiler volumes
- Food industry: Can sizes, drum volumes, silo capacities
- Construction: Column material requirements, concrete pillars
- Chemistry: Volumetric cylinder measurements in labs
- Everyday: Water bottle sizes, paint can volumes, fuel tanks