How many liters and cubes are in the barrel?

The volume of a barrel is, at first glance, a fairly simple value. In a cylindrical barrel with a constant diameter, it is easy to calculate. The old version, with curved walls, requires a special approach to calculating the volume.

In addition to a calculator, a tape measure comes in handy. Its length may not exceed 3 m.

To begin with, the diameter is measured in a cylindrical barrel. It is easy to spot by noticing the highest value.

If a thinner material was used, for example stainless steel up to 1 mm, then the thickness of the walls of the container can be neglected.

The diameter value measured for a specific container is halved. This is the radius of the product. The formula includes two calculations.

1. The square of the radius value is multiplied by the number 3.1415926535 ..., more approximate - 3.1416. This number is associated with the circumference - it is an infinite decimal fraction (an irrational value). The resulting value is the area of ​​a circle or base (bottom) in its true size.
2. We measure the height of the barrel - and multiply it by the resulting area of ​​the bottom. This is the volume of the container. The measured values ​​are converted into meters, otherwise the volume value in cubic meters will be unrealistically large.

For an old barrel with a variable diameter, we carry out a slightly different calculation.

1. We measure the diameter at the top - the smallest effective value. Above and below it will turn out to be the same - both bottoms of the container are also equal. Divide the diameter in half, square the resulting value and multiply by 3.1416.
2. Using a tape measure, we gird the barrel around and in the middle. The resulting value is the circumference. Dividing it by the number 3.1416, we get the diameter, we divide its value in half. This is the maximum radius of the container - its larger value. Subtract from the radius the thickness of the walls (curved boards forming the walls) - we get the real, effective value of the radius (at the maximum). Multiplying the number 3.1416 by the square of its value - we get the area of ​​a part of an imaginary plane passing through the middle of the barrel and bounded by the inner surface of its walls.
3. Determine the arithmetic mean (in square meters) of the larger and smaller effective values ​​of the base of the tank. That is, we add them - and we divide them in two.
4. We measure (in meters) and multiply the height value by the average area of ​​the bottom of the tank.

The resulting value is the volume of the "pot-bellied" container.

For an elliptical barrel, the counting scheme is different.

1. We measure the distance between the opposite points of the container located on the ellipse (oval of the cross section). You should get two noticeably different values.
2. Find out the arithmetic mean of these quantities, divide it in half again - this is the radius.
3. We measure the height - and multiply its value by the second power of the average radius and the number 3.1416. The resulting value - in cubic meters - is the volume of the oval container.

Although the concept of radius does not apply to an oval, it is easy to define it as an average. It is assumed that the oval is a perfect curve, resembling a flattened and elongated circle at the same time.

Tanks in the form of a prism (most often correct) are not very common, their calculation formula is complicated. To find their volume, the following geometric concepts have been introduced:

• the perimeter of the polygon is the base, the area of ​​which is needed to calculate the volume of the container;
• apothem is the length of the line segment connecting the center of the polygon with the middle of any of its sides.

To find the area of ​​the bottom, for example, a regular hexagonal prism, do 4 calculations.

1. Measure and calculate the perimeter of the bottom of the prismatic barrel.
2. Determine the center of the prism by drawing lines with a pencil connecting the opposite sides of the regular hexagon. The point of their intersection is the center of the bottom. Mark a point in the middle of either side of the bottom-hexagon and draw a line-apothem. Measure its length.
3. Divide the bottom perimeter in half - and multiply it by the apothem value. Do not forget to convert the measured values ​​into meters. The result is the area - in square meters - of the bottom of the barrel.
4. Multiply this value by the height.

The volume of the hexagonal prism container is calculated. For barrels with a base in the form of an irregular polygon, you will need to measure all sides of the bottom - and transfer them to the drawing, inscribe this polygon into a circle. The formula for calculating the volume of such a geometric figure can be somewhat complicated. But the industry almost does not produce such tanks, and the calculation of the "wrong" capacity is of more theoretical interest than practical.

Calculating the displacement means taking into account a constant value: 1 liter of water - 0.001 m3. A centner of water takes 0.1 cubic meters. This formula is valid for all liquids: one liter is a cubic decimeter. It is easy to calculate the cubic capacity, for example, of a tank carrying 4 tons of water: this is the same number of "cubes". But for, for example, oil, the "cube" weighs significantly less than one ton. The density of the same oil is as much less than the density of water, as the weight of a certain volume of oil products is lower than the mass of the same amount of water. But 1 m3 is a constant value.

For a water supply of one ton (1 m3), 5 such containers will be needed.