The cylinder volume formula will help to calculate the volume of the barrel for solving problems in order to find the total volume of a cylindrical object in different units expressed in liters (L), gallons, cubic inches, cubic feet from the given input values of the middle, upper or lower radius. This article will provide the barrel volume formula.
Geometric concept
In geometry, a barrel is a large round container, usually made of wood or metal, with flat ends and, as a rule, curved sides. A small barrel is called a cylinder. Below is the formula for the volume of the barrel and its phased calculation. The metrics provided allow users to understand how the values are used to calculate cylinder volumes.
Barrel and its formulas
The calculator uses mathematical formulas to find the total volume of a cylindrical object in liters and gallons. The formula for the volume of the barrel will be set by a clear example.
This step-by-step calculation can be useful for understanding how the values are used in the mathematical formula for the volume of the barrel in liters. Such calculations will help determine the volume of the cylindrical body.
Consider an example.
A cylindrical object is given having an average radius D = 18 inches, an upper and lower radius d = 15 inches, and a height h = 10 inches. It is required to answer the question posed: what is the volume of this subject?
Consider the solution.
Value data:
- average radius D = 18 inches;
- upper and lower radius d = 15 inches;
- height h = 10 inches.
Phased calculation
To calculate the volume of the barrel, the formula should be of this form:
(πh / 12) x (2D2 + d2)
Replace the values in the above formula = [(π x 10) / 12] [(2 x 182) + 152] = 2.61 x 873 = 2285.50 cubic inches.
1 cubic inch contains 0.016387 liters. To find the cylinder volume in liters, multiply 2285.50 inches by 0.016387 liters = 2285.50 x 0.016387 = 37.45 liters.
1 cubic inch contains 0.00432899 US gallons of liquid. To find the cylinder volume in US liquid gallons, multiply 2285.50 with 0.00432899 gallons = 2285.50 x 0.00432899 = 9.89 US liquid gallons.
If the input values are indicated in feet, it would be advisable to refer to the table below to calculate the conversion coefficient. The corresponding conversion factor should be multiplied by the result calculated by the above mathematical formula to find the volume.
The volume of the cylinder may be required for calculation in SI, metric or conventional systems, therefore the volume calculator is endowed with the function of converting the basic units of measurement to find the output values in different units, such as:
- liters (L);
- gallons (gallon);
- cubic inches (inches);
- cubic feet (feet);
- cubic meters (m);
- cubic centimeters (cm);
- cubic millimeters (mm).
Using the conversion table, you can determine the following indicators:
- 1 cubic inch = 0.016387 liters;
- 1 cubic inch = 0.00360464 gallon;
- 1 cubic inch = 0.00432899 US gallon;
- 1 cubic foot = 28.3168 liters;
- 1 cubic foot = 6.22884 gallon;
- 1 cubic foot = 7.48052 US gallon.
Be it a water tank, paint can or test tube, each cylindrical container has two common characteristics:
- circular cross section;
- a specific expansion in space, called its length or height.
If you need to know the capacity of the cylinder, how much it can accommodate, calculate its volume. There is a simple formula for this, but there is one caveat. It is important to consider the wall thickness of the container. In most cases, this amount is negligible, but not always. One more thing: capacity is usually measured in gallons or liters, so if you need these units, you will have to convert from cubic feet, inches or other metric units.
The formula V = πr2h or V = (πd2h) / 4 will help to calculate the volume. Since the thickness affects the external volume, it is necessary to measure the internal dimensions if the cylinder has thick walls.
Volume and thickness
The words “volume” and “capacity” are often used interchangeably, but they mean different things. The volume of the cylinder is equal to the amount of space occupied, it can be measured by immersing in water and setting the amount of water. If the cylinder is thick-walled, its thickness can vary significantly from volume.
Calculation of cylinder volume
The formula for calculating the volume of a cylinder with radius r and height h is as follows: V = πr2h.
In practice, it is difficult to measure the radius, because for this you need to accurately determine the center of the cylinder. It is much easier to measure the diameter, which is the maximum distance between the walls. Since the radius is half the diameter (d = 2r), the volume formula for the diameter looks like this:
V = π • (d / 2) 2 • h
This simplifies the calculations:
V = (πd2h) / 4
If the walls are thin, the volume is equal to the thickness, but if the walls are thick, the volume will be less.
Convert to gallons or liters
If measured in inches, the result will also be in these units. Similarly, by measuring in feet, centimeters or meters, the result is obtained in cubic centimeters or cubic meters, respectively.
To summarize
The drum volume calculation formula will help users understand how to manually calculate the volume, however, when it comes to performing quick calculations, a volume calculator may be useful for finding results.