Many building materials, fuel, food products are supplied to wholesale warehouses in containers of cylindrical or similar shape. These can be barrels, tanks or cans. In all such cases, to determine the quantity of a substance, it is necessary to first calculate the volume. The shape of such containers may differ slightly from the classic cylinder, and therefore the calculation methods will differ.

You will need

Length measuring tools;
- calculator.

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Instructions

The barrel may have a regular cylindrical shape. In this case, its base is a circle. If possible, find the center of the base, draw a diameter through it and measure. Divide it by 2. You get the radius. This can be done with a barrel lying on its side or upside down. When this is not possible, measure the circumference of the base and find the radius using the formula R=P/2?, where R is the radius of the base and P is the circumference.

Measure the height of the barrel. This is easiest to do with a tape measure. For accuracy, draw a line on the side that will be strictly perpendicular to the base. Calculate the volume of the barrel using the same formula as the volume of any other cylinder. V=?*R2*H, where V is the volume, R is the radius of the base of the barrel, H is the height.

The base of the barrel is not necessarily a circle, and the side surface may be curved. In this case, you need to take a few more measurements. If its sides are curved in a parabola or in a circular arc, calculate or measure the diameter of the middle section. Label the diameter of the base as D" and the area of ​​the middle section as D"".

Calculate the volume of a barrel, the side surface of which is curved along the arc of a circle, by multiplying the number? by 1/12 of the height and by the sum of twice the square of the diameter of the middle section and the square of the base. This can be expressed by the formula V=?*H/12*(2D""2+D"2), where H is the height, D" and D"" are the diameters of the base and middle section, respectively, and V is the volume.

Using a similar principle, the volume of a barrel is calculated, the side surface of which is curved along a parabola. Is it equal to the product of the number? by 1/15 of the height and the sum of twice the square of the base diameter, the product of both diameters and 0.75 square of the base diameter). This action can be indicated by the formula V=?*H/15*(2D""2+D"*D""+0.75D"2).

How simple

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Nowadays it is rare to find a real wooden barrel. The place of classic barrels has long been taken by their metal and plastic counterparts. As a rule, modern barrels are cylindrical in shape, so calculating the volume of such a vessel is very simple. But calculate the capacity of the old one,

To calculate the volume of any body, you need to know its linear dimensions. This applies to such figures as a prism, pyramid, sphere, cylinder and cone. Each of these figures has its own formula for determining volume. You will need - a ruler; - knowledge of properties volumetric figures; - formulas for the area of ​​a polygon.

Nowadays, it is rare to find a real wooden barrel. The place of classic barrels has long been taken by their metal and plastic counterparts. As a rule, modern barrels are cylindrical in shape, so calculating the volume of such a vessel is very simple. But not every mathematician can calculate the capacity of an old, pot-bellied barrel.

You will need

ruler, calculator, rope

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Instructions

If the barrel is cylindrical, measure its height and radius. For a thick-walled one, it is necessary to measure the inner radius in order to obtain its capacity, and not just the occupied volume. Convert the measurement results to meters. Then use the classic formula to calculate the volume of a cylinder:

Vcyl = ? *R? *H,

R – radius of the base (bottom) of the barrel,
H – barrel height,
Vcyl – volume of a cylindrical barrel,
? – the number “pi”, approximately equal to 3.14.

If it is difficult to measure the radius of the barrel, then measure its diameter. To do this, fix one end of a ruler or rope to the edge of the barrel. Then, by turning the ruler or string, find the farthest point on the opposite edge. Since the diameter of the barrel is twice its diameter, the formula for calculating the volume of the barrel will be similar:

Vcyl = ? * (D/2)? *H,

Vcyl = ? * ? *D? *H,

where: D – internal diameter of the barrel bottom.

If it is impossible to measure the diameter of the barrel, then determine the length of its circumference. To do this, take a fairly long rope (cord, twine, thread, etc.) and wrap it once around the barrel.

So what is the circumference of a circle? * D, then the diameter of the barrel will be equal to the length of its circumference divided by?. Those. D = L/?. To determine the volume of a barrel using the circumference, substitute this expression into the previous formula:

Vcyl = ? * ? *D? * H = ? * ? * (L/?)? * H = ? *L?/? *H,

where: L – circumference (girth) of the barrel.

If you need to calculate the volume of a classic (pot-bellied) barrel, then you should not study Kepler’s essay “Stereometry of Wine Barrels”. Just use a purely practical formula developed over several centuries by French winemakers:

Vb = 3.2 * r * R * H,

r is the radius of the barrel bottom, and

R is the radius of its widest part.

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

Vb = 0.8 * d * D * H.

How simple

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It is difficult for modern man to understand why vintage barrels had just such a “pot-bellied” shape. The point here is not the sophistication of ancient designers. In principle, truncated-conical containers would be suitable for this - it would be easier to assemble and the volume of such a barrel would not be difficult to find. However, it is unlikely that such a barrel would have been possible

A cubic meter (cubic meter) is a measure of volume adopted for use in the international metric system of units of measurement. That is, to determine the number of cubic meters of any material (for example, concrete, gas, wood, etc.), you should calculate the volume it occupies. Depending on the

Nowadays, it is rare to find a real wooden barrel. The place of classic barrels has long been taken by their metal and plastic counterparts. As a rule, modern barrels are cylindrical in shape, so calculating the volume of such a vessel is very simple. But not every mathematician can calculate the capacity of an old, pot-bellied barrel.

You will need

• ruler, calculator, rope

Instructions

• If the barrel is cylindrical, measure its height and radius. For a thick-walled one, it is necessary to measure the inner radius in order to obtain its capacity, and not just the occupied volume. Convert the measurement results to meters. Then use the classic formula to calculate the volume of the cylinder: Vcyl = π * R² * H, where: R is the radius of the base (bottom) of the barrel,
  H – barrel height,
  Vcyl – volume of a cylindrical barrel,
  π is the number “pi”, approximately equal to 3.14.
• If it is difficult to measure the radius of the barrel, then measure its diameter. To do this, fix one end of a ruler or rope to the edge of the barrel. Then, by turning the ruler or string, find the farthest point on the opposite edge. Since the diameter of the barrel is twice its diameter, the formula for calculating the volume of the barrel will be similar: Vcyl = π * (D/2)² * H, or: Vcyl = ¼ * π * D² * H,
  where: D – internal diameter of the barrel bottom.
• If it is impossible to measure the diameter of the barrel, then determine the length of its circumference. To do this, take a fairly long rope (cord, twine, thread, etc.) and wrap it once around the barrel.
  Since the circumference is equal to π * D, the diameter of the barrel will be equal to its circumference divided by π. Those. D = L/π. To determine the volume of the barrel through the circumference, substitute this expression into the previous formula: Vcyl = ¼ * π * D² * H = ¼ * π * (L/π)² * H = ¼ * L²/π * H, where: L – circumference (girth) of the barrel.
• If you need to calculate the volume of a classic (pot-bellied) barrel, then you should not study Kepler’s essay “Stereometry of Wine Barrels”. Just use a purely practical formula, derived over several centuries by French winemakers: Vb = 3.2 * r * R * H, where: 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 middle (D) of the barrel are known, then use the formula: Vb = 0.8 * d * D * H.