Advice 1: How to calculate the volume of the barrel

In our time is rarely where you can meet a real wooden barrel. Classic barrels for a long time took their metal and plastic counterparts. As a rule, modern barrels have a cylindrical shape, so to calculate the volume of this vessel is very simple. But to calculate the capacity of the old, "pot-bellied", the barrel will not everyone is a mathematician.
How to calculate the volume of the barrel
You will need
  • ruler, calculator, rope
If the barrel has a cylindrical shape, measure its height and radius. For thick-walled it is necessary to measure the inner radius to obtain its capacity and not just volume. Translate the results of the measurements to meters. Then use the formula to calculate volume of a cylinder:

Vцил = π * R2 * H,


R is the radius of the base (bottom) of the barrel,
H – height of the barrel,
Vцил – the volume of the cylindrical barrel,
π is the number PI, approximately equal to 3.14.
If the radius of the barrel is difficult to measure, then measure its diameter. To do this, clamp one end of a line or rope on the edge of the barrel. Then, turning the ruler or a rope, find the most distant point on the opposite edge. Since the barrel diameter is twice its diameter, the formula to calculate the volume of the barrel will be similar to:

Vцил = π * (D/2)2 * H,


Vцил = ¼ * π * D2 * H
where: D – inner diameter of the bottom of the barrel.
If the barrel diameter cannot be measured, then determine the length of its circumference. To do this, take a sufficiently long rope (cord, string, thread, etc.) and wrap it once around the barrel.
Since the circumference is π * D, the barrel diameter will be equal to the length of its circumference divided by π. I.e. D = L / π. To determine the volume of the barrel through the circumference, substitute this expression into the previous formula:

Vцил = ¼ * π * D2 * H = ¼ * π * (L/π)2 * H = ¼ * L2/π * H

where: L – the circumference (girth) of the barrel.
If you want to calculate the volume of a classical (pot-bellied) barrels, it is not necessary to examine the composition of Kepler's "Stereometry of wine barrels". Just use the purely practical formula is derived for several centuries winemakers of France:

Vб = 3,2 * r * R * H,


r is the radius of the bottom of the barrel, and
R is the radius of its widest part.

Accordingly, if only the diameters of the bottom (d) and mid (D) of the barrel, then use the formula:

Vб = 0,8 * d * D * H.

Advice 2: How to calculate the volume of a cylinder

Cylinder - a kind of geometric body which is formed of arranged parallel to each other circles, and the many parallel between a straight line drawn from one circle to another. Circles are called the bases of the cylinderand. In order to calculate the volume of a cylinder, it is sufficient to use the formula.
Cylinder with height h and radius of the circle r at the base
You will need
  • R is the radius of the circle lying at the base of the cylinder;
  • h - the height of the cylinder (the distance between the forming circles);
  • π is a constant (π = 3.14).
For example, in the space of a given cylinder whose base is the circle of radius R. the Height of the cylinder equal to h. Then, with these data, the volume of the cylinder V can be found as follows:
V = π*R2*h.
From the first formula we can deduce other, because we know that the area of a circle can be found as: S = π*R2, R2 = d2/4. From this it follows:
V = S*h
V = π*(d2/4)*h, where d - diameter of the base of the cylinder circumference.
Is the advice useful?