Volume of a Cylinder Calculator
Calculate the volume, total surface area, and lateral surface area of a cylinder from its radius and height. See also Volume of Cone Calculator and Volume of Sphere Calculator.
How to Calculate the Volume of a Cylinder
To find the volume of a cylinder, measure the radius of the circular base and the height (the perpendicular distance between the two bases). Square the radius, multiply by π, then multiply by the height. The total surface area includes both circular bases and the curved lateral surface. This calculator computes all three values automatically.
Cylinder Volume Formula
V = π × r² × h
Total SA = 2 × π × r × (r + h)
Lateral SA = 2 × π × r × h
Base Area = π × r²
Example
Find the volume of a cylinder with radius 4 and height 10:
V = π × r² × h
V = π × 4² × 10
V = π × 16 × 10
V ≈ 502.6548 cubic units
Cylinder Volume Reference Table
| Radius | Height | Volume | Surface Area |
|---|---|---|---|
| 1 | 5 | 15.7080 | 37.6991 |
| 2 | 5 | 62.8319 | 87.9646 |
| 3 | 5 | 141.3717 | 150.7964 |
| 4 | 5 | 251.3274 | 226.1947 |
| 5 | 5 | 392.6991 | 314.1593 |
| 2 | 10 | 125.6637 | 150.7964 |
| 4 | 10 | 502.6548 | 351.8584 |
| 5 | 10 | 785.3982 | 471.2389 |
| 6 | 10 | 1130.9734 | 603.1858 |
| 8 | 10 | 2010.6193 | 904.7787 |
| 5 | 15 | 1178.0972 | 628.3185 |
| 10 | 10 | 3141.5927 | 1256.6371 |
| 10 | 20 | 6283.1853 | 1884.9556 |
| 15 | 15 | 10602.8752 | 2827.4334 |
| 20 | 20 | 25132.7412 | 5026.5482 |
Solved Examples
Example 1: Water Tank Capacity
A cylindrical water tank has a radius of 1.5 m and height of 3 m. How many liters of water can it hold? (1 m³ = 1000 L)
V = π × 1.5² × 3
V = π × 2.25 × 3
V = π × 6.75
V ≈ 21.206 m³ = 21,206 liters
Example 2: Soda Can Volume
A standard soda can has a diameter of 6.6 cm and height of 12.1 cm. Calculate its volume.
Radius = 6.6 / 2 = 3.3 cm
V = π × 3.3² × 12.1
V = π × 10.89 × 12.1
V ≈ 413.82 cm³ ≈ 414 mL
Example 3: Grain Silo Capacity
A cylindrical grain silo has a diameter of 8 m and height of 15 m. Find the storage volume.
Radius = 8 / 2 = 4 m
V = π × 4² × 15
V = π × 16 × 15
V ≈ 753.98 m³
Example 4: Candle Wax Volume
A cylindrical candle has radius 2.5 cm and height 18 cm. How much wax is needed?
V = π × 2.5² × 18
V = π × 6.25 × 18
V ≈ 353.43 cm³
Practice Questions
Q1: Find the volume of a cylinder with radius 6 cm and height 14 cm.
Answer: V = π × 6² × 14 = π × 504 ≈ 1,583.36 cm³
Q2: A pipe has inner diameter 10 cm and length 2 m. What is its internal volume in liters?
Answer: r = 5 cm, h = 200 cm; V = π × 25 × 200 ≈ 15,707.96 cm³ ≈ 15.71 liters
Q3: A cylinder has volume 1000 cm³ and height 8 cm. What is the radius?
Answer: r = √(V / πh) = √(1000 / (π × 8)) = √(39.79) ≈ 6.31 cm
Q4: If both the radius and height of a cylinder are doubled, how does the volume change?
Answer: V₂ = π(2r)²(2h) = π × 4r² × 2h = 8πr²h = 8V₁. Volume increases 8×.
Q5: Calculate the lateral surface area of a cylinder with r=7 and h=10.
Answer: Lateral SA = 2πrh = 2 × π × 7 × 10 ≈ 439.82 square units
Q6: Two cylinders have the same volume. One has r=4, h=9. The other has r=6. Find its height.
Answer: π(4²)(9) = π(6²)(h); 144 = 36h; h = 4 units
Common Mistakes
Using diameter instead of radius: V = πr²h requires the radius. Using diameter directly gives 4× the correct volume.
Confusing height with slant height: For oblique cylinders, use the perpendicular height (not the slant). The height is the vertical distance between the two bases.
Forgetting to square the radius: The formula is πr²h, not πrh. Forgetting to square the radius underestimates the volume.
Unit inconsistency: If radius is in cm and height in m, convert to the same unit first. Mixed units produce meaningless results.
Key Takeaways
- Cylinder volume is V = πr²h — the base area (πr²) times the height.
- A cone with the same base and height has exactly 1/3 the cylinder volume.
- Doubling the radius quadruples the volume; doubling height only doubles it.
- Lateral surface area (2πrh) is the area of the curved side only.
- Convert diameter to radius (r = d/2) before applying the formula.
- 1 liter = 1000 cm³ — useful for capacity calculations.
Frequently Asked Questions
What is the volume of a cylinder?
The volume of a cylinder is the total three-dimensional space enclosed within its two circular bases and curved surface. It is calculated as V = πr²h, where r is the base radius and h is the height.
What is the difference between total and lateral surface area?
The lateral surface area is only the curved side of the cylinder (2πrh). The total surface area adds the two circular bases (2πr²), giving 2πr(r + h).
How do I find the volume if I know the diameter?
Divide the diameter by 2 to get the radius, then use V = πr²h. For example, a cylinder with diameter 8 and height 10 has radius 4, so V = π × 16 × 10 ≈ 502.65.
Does the formula work for oblique cylinders?
Yes, the volume formula V = πr²h works for oblique cylinders as long as h is the perpendicular height (not the slant height). The surface area formula, however, only applies to right cylinders.