How To Calculate Cylinder Volume
The volume of a cylinder can be calculated by multiplying the base area by the height. The mathematical expression is:
V = S × h = π × r² × h
Where:
- V: The volume of the cylinder.
- S: The base area of the cylinder.
- h: The height of the cylinder.
- r: The radius of the cylinder's base.
- π: Pi, generally approximated as 3.14 (or more precise values can be used).
For example, if the base radius of a cylinder is 5 cm and the height is 10 cm, the volume can be calculated as:
V = π × 5² × 10 = 3.14 × 25 × 10 = 785 cm³
How To Calculate Hollow Cylinder Volume
A hollow cylinder, also known as an annular cylinder, has an outer and an inner circle. The volume of a hollow cylinder can be calculated by subtracting the volume of the inner cylinder from the volume of the outer cylinder. The formula is:
V_hollow = V_outer - V_inner = π × R2² × h - π × R1² × h = π × h × (R2² - R1²)
Where:
- V_outer: The volume of the outer cylinder.
- V_inner: The volume of the inner cylinder.
- R2: The radius of the outer cylinder's base.
- R1: The radius of the inner cylinder's base.
- h: The height of the cylinder.
For example, if a hollow cylinder has an outer radius of 10 cm, an inner radius of 5 cm, and a height of 20 cm, the volume can be calculated as:
V_hollow = π × 20 × (10² - 5²) = 3.14 × 20 × (100 - 25) = 3.14 × 20 × 75 = 4710 cm³
How To Calculate Half Cylinder Volume
The volume of a half cylinder can be calculated by finding the volume of a full cylinder and then dividing it by 2. Alternatively, you can use the formula specifically for a half cylinder. The mathematical expression is:
V = (π × r² × h) ÷ 2
Or, using the formula for a half cylinder:
V = π × r² × h ÷ 2 = (1/2) × π × r² × h
Where:
- V: The volume of the half cylinder.
- r: The radius of the cylinder's base.
- h: The height of the cylinder.
- π: Pi, generally approximated as 3.14 (or more precise values can be used).
For example, if the base radius of a half cylinder is 5 cm and the height is 10 cm, the volume can be calculated as:
V = (π × 5² × 10) ÷ 2 = (3.14 × 25 × 10) ÷ 2 = 392.5 cm³
Or using the half cylinder formula:
V = (1/2) × π × 5² × 10 = (1/2) × 3.14 × 25 × 10 = 392.5 cm³
How To Calculate Volume of Cylinder in Gallons
The volume of a cylinder in gallons can be calculated by first finding the volume in cubic units and then converting those units to gallons. The mathematical expression for the volume of a cylinder in cubic units is:
V = π × r² × h
Where:
- V: The volume of the cylinder in cubic units.
- r: The radius of the cylinder's base.
- h: The height of the cylinder.
- π: Pi, generally approximated as 3.14 (or more precise values can be used).
Once you have the volume in cubic units, you can convert it to gallons using the appropriate conversion factor. For example, if you have the volume in cubic centimeters, you can convert it to gallons using the fact that 1 gallon is approximately equal to 3,785.41 cubic centimeters.
For example, if the base radius of a cylinder is 5 cm and the height is 10 cm, the volume in cubic centimeters can be calculated as:
V = π × 5² × 10 = 3.14 × 25 × 10 = 785 cm³
To convert this to gallons, you would use the conversion factor:
Volume in gallons = Volume in cm³ ÷ 3,785.41
So, the volume of the cylinder in gallons would be:
Volume in gallons = 785 cm³ ÷ 3,785.41 ≈ 0.207 gallons
How To Calculate Volume of Cylinder in Litres
The volume of a cylinder in litres can be calculated by first finding the volume in cubic units and then converting those units to litres. The mathematical expression for the volume of a cylinder in cubic units is:
V = π × r² × h
Where:
- V: The volume of the cylinder in cubic units.
- r: The radius of the cylinder's base.
- h: The height of the cylinder.
- π: Pi, generally approximated as 3.14 (or more precise values can be used).
Once you have the volume in cubic units, you can convert it to litres using the appropriate conversion factor. For example, if you have the volume in cubic centimeters, you can convert it to litres using the fact that 1 litre is equal to 1,000 cubic centimeters.
For example, if the base radius of a cylinder is 7 cm and the height is 12 cm, the volume in cubic centimeters can be calculated as:
V = π × 7² × 12 = 3.14 × 49 × 12 = 1,846.32 cm³
To convert this to litres, you would use the conversion factor:
Volume in litres = Volume in cm³ ÷ 1,000
So, the volume of the cylinder in litres would be:
Volume in litres = 1,846.32 cm³ ÷ 1,000 = 1.84632 litres
Rounding to two decimal places, the volume of the cylinder is approximately 1.85 litres.
Commonly seen cylindrical objects in daily life
| # | Cylindrical Object | Description |
|---|---|---|
| 1 | Soda Can | A cylindrical container for beverages, designed for easy grip and storage. |
| 2 | Bucket | A cylindrical container used for carrying liquids or other materials. |
| 3 | Candle | Pillar-shaped candles often used for lighting or decoration. |
| 4 | Pipe | A hollow cylinder used for transporting fluids or gases. |
| 5 | Trash Bin | A cylindrical container for disposing of waste. |
| 6 | Drum | Cylindrical containers like oil barrels or musical drums. |
| 7 | Battery | Cylindrical batteries such as AA or AAA types, commonly used in devices. |
| 8 | Cylindrical Vase | A vase with a cylindrical shape, often used for flowers or decoration. |
| 9 | Kitchen Utensils | Cylindrical items like rolling pins or spice containers. |
| 10 | Water Tank | Large cylindrical containers used for storing water. |
Unit Conversion Table in Volume of Cylinder
| From Unit | To Unit | Conversion Factor | Formula |
|---|---|---|---|
| \(\text{cm}^3\) | \(\text{dm}^3\) | 0.001 | \(V_{\text{dm}^3} = \frac{V_{\text{cm}^3}}{1000}\) |
| \(\text{dm}^3\) | \(\text{m}^3\) | 0.001 | \(V_{\text{m}^3} = \frac{V_{\text{dm}^3}}{1000}\) |
| \(\text{cm}^3\) | \(\text{m}^3\) | 0.000001 | \(V_{\text{m}^3} = \frac{V_{\text{cm}^3}}{1,000,000}\) |
| \(\text{in}^3\) | \(\text{ft}^3\) | 0.000578704 | \(V_{\text{ft}^3} = \frac{V_{\text{in}^3}}{1728}\) |
| L | \(\text{cm}^3\) | 1000 | \(V_{\text{cm}^3} = V_{\text{L}} \times 1000\) |
| gal (US) | L | 3.78541 | \(V_{\text{L}} = V_{\text{gal}} \times 3.78541\) |
| gal (UK) | L | 4.54609 | \(V_{\text{L}} = V_{\text{gal (UK)}} \times 4.54609\) |
| \(\text{m}^3\) | \(\text{ft}^3\) | \(\approx\) 35.3147 (approx.) or 0.0283168-1 (precise) |
Approx.: \(V_{\text{ft}^3} \approx V_{\text{m}^3} \times 35.3147\) Precise: \(V_{\text{ft}^3} = \frac{V_{\text{m}^3}}{0.0283168}\) |
Cylinder Userful Chart
| Topic | Key Points |
|---|---|
| Cylinders in Nature | Tree trunks & plant stems, some bones (and bodies), flagella of microscopic organisms |
| Drawing a Cylinder | 1. Draw a slightly flattened circle. 2. Draw two equal, parallel lines from the far sides of the circle. 3. Link the ends with a semi-circular line. 4. Add shadow and shading as appropriate. |
| Calculating Cylinder Weight | Radius² × π × Height × Density = Weight |
| Surface Area to Volume Ratio | Volume: πr²h, Surface Area: 2πrh + 2πr², Ratio: πr²h : 2πrh + 2πr² or simplified to rh : 2(h+r) |
| Calculating Cylinder Height | Known Volume and Radius: Volume ÷ (π × Radius²) = Height Known Surface Area and Radius: (Surface Area - 2πr²) ÷ (2πr) = Height |
| Calculating Cylinder Radius | Known Volume and Height: Volume ÷ (π × Height) then square root = Radius Known Surface Area and Height: Solve quadratic equation using Surface Area = 2πrh + 2πr² |
| Oval Cylinder Volume | (Minor Axis × Major Axis) × π ÷ 4 × Height = Volume |
| Slanted Cylinder Volume | Radius² × π × sin(Angle) × Side Length = Volume |
| Swept Volume Calculation | (Bore Diameter ÷ 2)² × π × Stroke Length = Swept Volume |