What is the volume of a cylinder?
The volume of a cylinder is the amount of space enclosed inside it. It is measured in cubic units (cm³, m³, liters). A cylinder has two circular bases connected by a curved lateral surface. The volume depends on the radius of the base and the height of the cylinder.
How do you calculate the volume of a cylinder?
Use the formula V = π × r² × h, where r is the radius of the base and h is the height.
- Measure the radius r (half the diameter) and height h
- Square the radius: r²
- Multiply by π (≈ 3.14159) and the height: V = π × r² × h
Example: a cylinder with radius 5 cm and height 10 cm has volume V = π × 25 × 10 ≈ 785.4 cm³.
What is the cylinder surface area formula?
A cylinder has three surface components:
- Base area (one circle): A = π × r²
- Lateral (curved) surface area: A = 2 × π × r × h
- Total surface area: A = 2 × π × r × (r + h)
The total surface area combines the two circular bases and the lateral surface that wraps around the cylinder.
What are some cylinder volume calculation examples?
- Soda can (r = 3.3 cm, h = 12.2 cm): V = π × 3.3² × 12.2 ≈ 417.5 cm³ ≈ 0.42 liters
- Water tank (r = 0.5 m, h = 2 m): V = π × 0.25 × 2 ≈ 1.57 m³ ≈ 1 570 liters
- Candle (r = 4 cm, h = 20 cm): V = π × 16 × 20 ≈ 1 005.3 cm³
When is a cylinder volume calculator useful?
Knowing the volume and surface area of a cylinder is useful in many situations:
- Estimating how much liquid a tank, barrel or container can hold
- Calculating how much material is needed to manufacture cylindrical packaging
- Determining the capacity of pipes, tubes and storage silos
- Solving geometry homework involving 3D shapes — see also our mean, median and mode calculator for data analysis or the percentage calculator to express volume ratios
What is the difference between lateral surface area and total surface area?
The lateral surface area (also called curved surface area) is only the side of the cylinder — the rectangle that wraps around the outside. Its formula is 2πrh. The total surface area adds the two circular base caps: 2πrh + 2πr². Use total surface area when calculating how much material covers the entire cylinder, and lateral surface area when the top and bottom are open (e.g., a pipe).
What is the volume of a hollow cylinder?
A hollow cylinder (like a pipe or tube) has an outer radius R and an inner radius r. The volume of the wall material is: V = π × (R² − r²) × h. To find the capacity of the hollow space, use only the inner radius: V_inner = π × r² × h. Example: a steel pipe with outer radius 5 cm, inner radius 4 cm and length 50 cm has a wall material volume of V = π × (25 − 16) × 50 ≈ 1 413.7 cm³, while its hollow interior holds V = π × 16 × 50 ≈ 2 513.3 cm³.