Presently it is already rare where it is possible to meet the real wooden barrel. The place of classical barrels was taken long ago by their metal and plastic analogs. As a rule, modern barrels have the cylinder form therefore it is very simple to calculate the volume of such vessel. And here to consider capacity ancient, "big-bellied", barrels not each mathematician will be able.
It is required to you
- ruler, calculator, rope
Instruction
1. If the barrel has the cylindrical form, then measure its height and radius. For thick-walled it is necessary to measure internal radius to receive its capacity, and not just occupied volume. Transfer results of measurements to meters. Then use a classical formula for calculation of volume of a cylinder: Vtsil = π * R² * H, where: R – radius of the basis (bottom) of a barrel, N – height of a barrel, Vtsil – the volume of a cylindrical barrel, π – number "пи", approximately equal 3.14.
2. If it is difficult to measure the radius of a barrel, then measure its diameter. For this purpose record one end of a ruler or a rope on the edge of a barrel. Then, turning a ruler or a rope, find the most remote point at the opposite edge. As diameter of a barrel is twice more than its diameter, the formula for calculation of volume of a barrel will be similar: Vtsil = π * (D/2)² * H, or: Vtsil = ¼ * π * D² * H, where: D – internal diameter of a bottom of a barrel.
3. If diameter of a barrel cannot be measured, then determine length of its circle. For this purpose take rather long rope (cord, a cord, a thread, etc.) and wind its once around a barrel. As length of a circle is equal π * to D, diameter of a barrel will be equal to length of its circle divided on π. I.e. D = L/π. To determine barrel volume through circle length, substitute this expression in the previous formula: Vtsil = ¼ * π * D² * H = ¼ * π * (L/π)² * H = ¼ * L²/π * H, where: L – length of a circle (grasp) of a barrel.
4. If it is necessary to calculate the volume of a classical (big-bellied) barrel, then you should not study Kepler's composition "Stereometry of wine casks". Just use purely practical formula removed for several centuries by wine makers of France: Vb = 3.2 * r * R * H, where: r – radius of a bottom of a barrel, aR is radius her a wide part. Respectively, if only diameters of a bottom (d) and the middle (D) barrel are known, then use a formula: Vb = 0.8 * d * D * H.