How to find the capacity of a cylindrical tank?

The capacity of a cylindrical tank is found by calculating its volume, which represents the total amount of substance it can hold.

Understanding Cylindrical Tank Capacity

The capacity of any container, including a cylindrical tank, is its internal volume. This volume determines how much liquid, gas, or other material it can contain. For a cylindrical tank, this calculation relies on its dimensions: the radius and its length (or height).

The Formula for Cylindrical Volume

To find the capacity of a cylindrical tank, you must use the formula for the volume of a cylinder. According to WorkSafe Victoria, the formula is:

Volume of Cylinder = πr² x Length

Where:

π (pi): A mathematical constant approximately equal to 3.14159.
r: The radius of the cylinder's base (half of its diameter).
Length: The length or height of the cylindrical tank.

Step-by-Step Calculation

Calculating the capacity of a cylindrical tank is a straightforward process involving a few key measurements and a simple formula.

Step 1: Measure the Radius (r)

The first crucial step is to determine the radius of the tank.

Measure the diameter: Use a tape measure to find the diameter of the circular base of the cylinder. This is the widest point across the circle.
Calculate the radius: The radius (r) is precisely half of the diameter. As specified by WorkSafe Victoria, you should "Measure the radius (half of the diameter) of the cylinder in centimetres, this value is 'r' in the formula."
Example: If the diameter is 100 cm, then the radius r = 100 cm / 2 = 50 cm.

Step 2: Measure the Length (or Height) of the Cylinder

Next, measure the total length of the cylindrical tank.

This is the distance from one end of the cylinder to the other. If the tank is standing upright, this measurement is its height.
Ensure that this measurement is in the same units as your radius (e.g., if radius is in centimeters, length should also be in centimeters).

Step 3: Apply the Formula

Once you have both r and Length (or height) in consistent units, you can plug these values into the volume formula.

Calculation: Multiply pi (π) by the square of the radius (r²) and then multiply that result by the length (Length).
Example (cont.): If r = 50 cm and Length = 200 cm:
- Volume = π (50 cm)² 200 cm
- Volume = π 2500 cm² 200 cm
- Volume = 500,000π cm³
- Volume ≈ 500,000 * 3.14159 cm³
- Volume ≈ 1,570,795 cm³

Step 4: Convert Units (Optional but Recommended)

The calculated volume will be in cubic units (e.g., cubic centimeters, cubic meters, cubic feet). To express capacity in more common units like liters or gallons, you'll need to perform a conversion.

Common Conversions:
- 1 cubic centimeter (cm³) = 0.001 liters
- 1 cubic meter (m³) = 1000 liters
- 1 cubic foot (ft³) ≈ 7.48 US gallons
Example (cont.): To convert the calculated volume from cubic centimeters to liters:
- Capacity in Liters = 1,570,795 cm³ / 1000 cm³/liter
- Capacity ≈ 1570.795 liters

Practical Example

Let's calculate the capacity of a water tank with the following dimensions:

Diameter: 120 cm
Length (Height): 180 cm

Calculate Radius (r):
r = Diameter / 2 = 120 cm / 2 = 60 cm
Apply the Volume Formula:
Volume = π * r² * Length
Volume = π * (60 cm)² * 180 cm
Volume = π * 3600 cm² * 180 cm
Volume = 648,000π cm³
Volume ≈ 648,000 * 3.14159 cm³
Volume ≈ 2,035,750.8 cm³
Convert to Liters:
Capacity in Liters = 2,035,750.8 cm³ / 1000 cm³/liter
Capacity ≈ 2035.75 liters

Therefore, the cylindrical tank has a capacity of approximately 2035.75 liters.

Essential Tips for Accuracy

To ensure the most accurate capacity calculation for your cylindrical tank, keep these tips in mind:

Precise Measurements: Use a reliable measuring tape and take multiple measurements to ensure accuracy, especially for the diameter and length.
Consistent Units: Always use the same units for both radius and length (e.g., both in centimeters, both in meters, or both in inches). Mixing units will lead to incorrect results.
Value of Pi (π): For practical purposes, using 3.14159 or the π button on a calculator will provide sufficient accuracy.
Internal Dimensions: For true capacity, measure the internal diameter and length of the tank, as the thickness of the tank walls will reduce the usable volume.

Here's a quick reference for common unit conversions:

Unit Measured	Volume Calculated (Cubic Unit)	Common Capacity Unit	Conversion Factor
Centimeters	Cubic Centimeters (cm³)	Liters	1 cm³ = 0.001 L
Meters	Cubic Meters (m³)	Liters	1 m³ = 1000 L
Inches	Cubic Inches (in³)	US Gallons	1 in³ ≈ 0.004329 US Gallons
Feet	Cubic Feet (ft³)	US Gallons	1 ft³ ≈ 7.48 US Gallons

For more information, you can refer to the WorkSafe Victoria guidelines on calculating cylinder or tank capacity.