Cylinder Volume Calculator
This calculator finds the volume and total surface area of a right circular cylinder based on its radius and height.
Relation to "Volume of a Circle": A cylinder has circular bases. Sometimes searches for "volume of a circle" might relate to the volume of a cylinder, which is essentially the area of the circular base (π * r²) multiplied by the height (h). Remember, a 2D circle itself only has area.
Enter the radius (r) and height (h) of the cylinder below to calculate its Volume (V) and Total Surface Area (SA). The correct cylinder volume formula is used.
Enter Cylinder Dimensions
Understanding Cylinder Volume & Formulas
What is a Cylinder?
A cylinder in its simplest form is defined as the surface formed by points at a fixed distance from a given straight line axis. In common use, "cylinder" refers to a right circular cylinder, where the bases are two parallel circles of equal size connected through their centers by an axis perpendicular to the planes of its bases. It has a given height (h) and radius (r).
The Cylinder Volume Formula
The formula for volume of cylinder is calculated by multiplying the area of its circular base by its height:
V = Base Area * Height = (π * r²) * h
Where:
- V is the Volume
- π (Pi) is approximately 3.14159...
- r is the radius of the circular base
- h is the height of the cylinder
This cylinder volume equation calculates the 3D space inside the cylinder.
Cylinder Total Surface Area Formula
The total surface area includes the area of the two circular bases and the area of the side (lateral surface):
SA = (2 * π * r²) + (2 * π * r * h)
Where SA is Total Surface Area, π is Pi, r is the radius, and h is the height.
Example Calculation (Provided in Original Text)
EX: Caelum uses cylindrical barrels with radius 3 ft and height 4 ft. Calculate the volume:
1. Radius (r) = 3 ft, Height (h) = 4 ft
2. Formula: V = π * r² * h
3. Calculation: V = π * (3)² * 4 = π * 9 * 4 = 36π
4. Result: V ≈ 113.1 cubic feet (ft³).
Real-Life Cylinder Volume Examples
Click on an example to see the step-by-step calculation:
Example 1: Soup Can Volume
Scenario: Find the volume of a standard soup can.
1. Known Values: Diameter ≈ 3 inches (so Radius r = 1.5 inches), Height (h) ≈ 4.5 inches.
2. Formula: V = π * r² * h
3. Calculation: V = π * (1.5)² * 4.5 ≈ π * 2.25 * 4.5 = 10.125π
4. Result: V ≈ 31.81 cubic inches.
Conclusion: A typical soup can holds about 32 cubic inches.
Example 2: Drinking Glass Volume (Idealized)
Scenario: Estimate the volume of a cylindrical drinking glass.
1. Known Values: Radius (r) ≈ 1.5 inches, Height (h) ≈ 6 inches.
2. Formula: V = π * r² * h
3. Calculation: V = π * (1.5)² * 6 ≈ π * 2.25 * 6 = 13.5π
4. Result: V ≈ 42.41 cubic inches (about 23 fluid ounces).
Conclusion: The glass can hold approximately 42 cubic inches.
Example 3: Oil Drum Volume (55 Gallon)
Scenario: Calculate the approximate volume of a standard 55-gallon oil drum.
1. Known Values: Diameter ≈ 22.5 inches (r = 11.25 inches), Height (h) ≈ 33.5 inches.
2. Formula: V = π * r² * h
3. Calculation: V = π * (11.25)² * 33.5 ≈ π * 126.5625 * 33.5 ≈ 4239.84π
4. Result: V ≈ 13320 cubic inches. (Note: 1 US gallon ≈ 231 cubic inches, so 13320 / 231 ≈ 57.6 gallons - close to the nominal 55 gallons).
Conclusion: A 55-gallon drum has an internal volume of roughly 13,300 cubic inches.
Example 4: Round Cake Layer Volume
Scenario: Find the volume of batter needed for a 9-inch round cake layer.
1. Known Values: Diameter = 9 inches (r = 4.5 inches), Height (h) ≈ 2 inches.
2. Formula: V = π * r² * h
3. Calculation: V = π * (4.5)² * 2 ≈ π * 20.25 * 2 = 40.5π
4. Result: V ≈ 127.23 cubic inches (about 5.5 US cups).
Conclusion: A 9x2 inch cake layer has a volume of about 127 cubic inches.
Example 5: US Quarter Coin Volume
Scenario: Calculate the volume of metal in a US quarter (a very short cylinder).
1. Known Values: Diameter ≈ 0.955 inches (r ≈ 0.4775 inches), Height (h) ≈ 0.069 inches.
2. Formula: V = π * r² * h
3. Calculation: V = π * (0.4775)² * 0.069 ≈ π * 0.228 * 0.069 ≈ 0.0157π
4. Result: V ≈ 0.049 cubic inches.
Conclusion: A US quarter has a tiny volume of about 0.05 cubic inches.
Example 6: Large Water Tank Volume
Scenario: Find the volume of a cylindrical water storage tank.
1. Known Values: Radius (r) = 1 meter, Height (h) = 2 meters.
2. Formula: V = π * r² * h
3. Calculation: V = π * (1)² * 2 = 2π
4. Result: V ≈ 6.28 cubic meters (or 6,283 Liters).
Conclusion: The tank holds approximately 6.3 cubic meters of water.
Example 7: Coffee Mug Volume
Scenario: Estimate the volume of a standard coffee mug.
1. Known Values: Diameter ≈ 8 cm (r = 4 cm), Height (h) ≈ 9.5 cm.
2. Formula: V = π * r² * h
3. Calculation: V = π * (4)² * 9.5 = π * 16 * 9.5 = 152π
4. Result: V ≈ 477.5 cubic cm (or 477.5 mL).
Conclusion: A standard mug holds about 475 mL.
Example 8: Volume Inside PVC Pipe Section
Scenario: Calculate the internal volume of a 1-foot long section of PVC pipe.
1. Known Values: Assume Inner Radius (r) = 1 inch, Length/Height (h) = 1 foot = 12 inches.
2. Formula: V = π * r² * h
3. Calculation: V = π * (1)² * 12 = 12π
4. Result: V ≈ 37.7 cubic inches.
Conclusion: A 1-foot section of 1-inch radius pipe holds about 38 cubic inches.
Example 9: Tree Trunk Volume (Approximate)
Scenario: Estimate the volume of wood in a section of a tree trunk, approximating it as a cylinder.
1. Known Values: Diameter = 2 feet (r = 1 foot), Height (h) = 10 feet.
2. Formula: V = π * r² * h
3. Calculation: V = π * (1)² * 10 = 10π
4. Result: V ≈ 31.42 cubic feet.
Conclusion: The tree trunk section contains roughly 31 cubic feet of wood.
Example 10: Roll of Paper Towels (Volume of Cylinder)
Scenario: Find the total cylindrical volume occupied by a full roll of paper towels (including the cardboard tube).
1. Known Values: Outer Diameter ≈ 5 inches (r = 2.5 inches), Height (h) = 11 inches.
2. Formula: V = π * r² * h
3. Calculation: V = π * (2.5)² * 11 ≈ π * 6.25 * 11 = 68.75π
4. Result: V ≈ 215.98 cubic inches.
Conclusion: The entire paper towel roll occupies about 216 cubic inches of space.
Understanding Volume Measurement
Volume is the quantification of the three-dimensional space a substance occupies...
Common Volume Units Reference
Ensure your input radius and height use a consistent unit...
Frequently Asked Questions about Cylinder Volume
1. What is the formula for volume of a cylinder?
The volume (V) of a cylinder is calculated using the formula: V = π * r² * h, where 'π' is Pi (approx. 3.14159), 'r' is the radius of the circular base, and 'h' is the height of the cylinder.
2. How do I find the volume if I know the diameter (d) instead of the radius?
The radius is half the diameter (r = d/2). You can calculate the radius first and then use the volume formula, or use a combined formula: V = π * (d/2)² * h = (π * d² * h) / 4.
3. Is this calculator related to the "volume of a circle"?
A cylinder has circular bases. Its volume formula (V = Base Area * Height) uses the area of that circle (Area = π * r²). So, while a circle itself doesn't have volume, its area is fundamental to calculating a cylinder's volume.
4. What's the difference between Cylinder Volume and Cylinder Surface Area?
Volume measures the space *inside* the cylinder (like how much water it can hold). Surface Area measures the total area of its outer surfaces (the top and bottom circles plus the curved side). This calculator provides both.
5. What units should I use for radius and height?
Use any consistent unit of length (e.g., cm, inches, meters). If you use centimeters for both radius and height, the volume will be in cubic centimeters (cm³ or mL) and the surface area in square centimeters (cm²).
6. What is the formula for the Total Surface Area of a cylinder?
The total surface area (SA) is the area of the two circular bases plus the area of the rectangular side when unrolled: SA = (2 * π * r²) + (2 * π * r * h).
7. What does 'right circular cylinder' mean?
It means the circular bases are directly aligned above each other, and the sides are perpendicular (at a right angle) to the bases. This calculator assumes a right circular cylinder.
8. Can I calculate the volume of an oval cylinder (elliptical base)?
No, this calculator is specifically for cylinders with circular bases. The volume of an elliptical cylinder requires the lengths of the semi-axes of the ellipse (a and b) instead of a single radius: V = π * a * b * h.
9. What if the top and bottom circles have different radii?
That shape is called a conical frustum, not a cylinder. A different formula is needed for its volume (this calculator doesn't handle frustums; see multi-shape calculators).
10. How does height affect the volume?
Volume is directly proportional to height. If you double the height while keeping the radius the same, you double the volume.
11. How does radius affect the volume?
Volume depends on the square of the radius (r²). If you double the radius while keeping the height the same, the volume increases by a factor of four (2² = 4).
