You will need

- roulette,
- calculator,
- - Handbook of elementary mathematics.

Instruction

1

Capacity in the form of a cylinder.

Measure tape measure the height and base diameter of the cylinder – usually, this form have the gas cylinders, drums and tank cars for different liquids, and glass, plastic and metal cans for canned food. Divide the diameter by two to get the radius. Multiply area of base of cylinder (area of a circle is equal to 3, 14* radius squared) to its height. This is the volume of the cylinder.

Measure tape measure the height and base diameter of the cylinder – usually, this form have the gas cylinders, drums and tank cars for different liquids, and glass, plastic and metal cans for canned food. Divide the diameter by two to get the radius. Multiply area of base of cylinder (area of a circle is equal to 3, 14* radius squared) to its height. This is the volume of the cylinder.

2

Capacity in the form of a cone.

Measure tape measure the base diameter and the height of the cone. Use the calculator to calculate the volume of the container. It is equal to one third the product of area of base (circle) and the height of the cone.

Measure tape measure the base diameter and the height of the cone. Use the calculator to calculate the volume of the container. It is equal to one third the product of area of base (circle) and the height of the cone.

3

Capacity in the form of a ball.

Tape measure measure the diameter of the ball. If it is difficult to execute, measure length of a circle – clasp your roulette ball at the equator or the zero Meridian, i.e. in the place where the circumference is maximum. In order to calculate the diameter, the resulting value is divided by the number of "PI", that is 3,14. Divide the diameter in half – this will be the radius. The volume of a sphere is equal to 4/3 works of PI and the radius of the ball in the cube.

Tape measure measure the diameter of the ball. If it is difficult to execute, measure length of a circle – clasp your roulette ball at the equator or the zero Meridian, i.e. in the place where the circumference is maximum. In order to calculate the diameter, the resulting value is divided by the number of "PI", that is 3,14. Divide the diameter in half – this will be the radius. The volume of a sphere is equal to 4/3 works of PI and the radius of the ball in the cube.

4

Capacity in the form of a parallelepiped.

A tape measure, measure the width, height and length of the parallelepiped, that is, three sides, having one common point. Multiply the values obtained. This will be the highest volume of containers of this type, often used for storage and transportation of various liquids.

A tape measure, measure the width, height and length of the parallelepiped, that is, three sides, having one common point. Multiply the values obtained. This will be the highest volume of containers of this type, often used for storage and transportation of various liquids.

Note

In calculations, all measurements of the geometric dimensions must be in the same units (millimeters, centimeters or meters).

Useful advice

For more complex forms of containers, they should be divided into such geometric shapes, with reference on mathematics available ready-made formula for calculating the volume (sphere, cylinder, pyramid, parallelepiped, etc.). Calculating separately the volumes of the components of the figures and after adding them together you get a tank volume of complex shape.

# Advice 2: How to calculate the volume of a cube

Calculate the volume

**of a cube**may be necessary not only in solving mathematical problems. For example, you need to know how many bricks in a package of the cubic form or how much liquid or dry ingredients will fit into a container. For this course, you will need to clear up a few options, but first, you need to calculate the volume**of a cube**.You will need

- To recall the definition and properties of a cube
- Measuring device

Instruction

1

Remember what CC It is a right hexahedron — geometric solid, each face of which represents a square. Since all sides

**of a cube**are the same — and faces his equal, as were the ribs. That is, to determine the volume you need to know the size of only one face.2

Remember, what is the volume of the parallelepiped. It is equal to the area of the base multiplied by the height. But

**the cube**length, width and height are equal. The cube can be put on any face, all the same, the footprint will be the same as in the original position. Indicate the edge**of the cube**as well. Find the area of the base. It is equal to the product of the length by the width, that is, S=a2..3

Calculate the volume by multiplying the area of the base A2 at the height which in this case is also equal. Accordingly, the volume V is equal to the size of the edge

**of the cube**erected in the third degree. V=a3.4

If you need to calculate the amount of a substance, which is supposed to fill a container of cubic shape, it is necessary to know the density of the substance. This number will be equal to the density multiplied by the volume

**of the cube**. And in order to calculate, for example, the number of bricks in a container of cubic shape, it is necessary to calculate the volume of each brick, then divide the volume of the container to the volume of the brick.Note

In some cases it is necessary to find the volume and the area of the walls - for example, when calculating the number of glass for the aquarium. Since all faces of a cube are the same, the square sum of the areas of the 6 faces, that is expressed by the formula S=6a2

Useful advice

Try practical measurements as accurate as possible. You can use a ruler, tape measure, bar-compass. Importantly, the division met the standards.

# Advice 3: How to calculate the volume of gas

To calculate the volume

**of gas**which is in a vessel or area, find the volume of geometric methods. This is due to the fact that gas always occupies the entire allotted amount. In that case, if you know the amount of a substance or the mass of gas in normal conditions, find the volume of the gas, multiplying the amount of matter in 0,0224 m3. If the gas is not in perfect conditions, use a special equation.You will need

- tape measure or range finder, thermometer, pressure gauge, periodic table.

Instruction

1

Calculation of gas volume geometric macadamias vessel filled with gas, find its volume. For example, if the room has a parallelepiped shape with a tape or rangefinder, determine the length, width and height in meters. The obtained results multiply and get the volume of gas in the room expressed in m3. If the vessel is cylindrical, measure its diameter, erect it in the square, multiply by 3.14, and height of the cylinder, which also measure the number you divide by 4.

2

Calculate the volume of a known mass of a particular gas in a normal usloviahtabl gas is in normal conditions (0o C, 760 mm. art), known for its mass and chemical formula using the periodic table determine the molar mass, given the fact that most of the simple gases of diatomic molecules. Then the mass of gas divide by its molar mass, and the resulting number multiply by 0,0224. Get the volume of gas in m3. There is another way. If you know the mass and type of gas, according to a special table to find the density and divide the mass of gas on its density. Get the volume of gas. If the gas mass is given in kilograms, take the density in kilograms per cubic meter, if in grams in grams per cubic centimeter. Accordingly, will the volume or in metres, or in cubic centimeters.

3

Calculation of the mass of gas through uravneniyakh a known mass of gas is in real conditions, find the number of substances for which the mass divide by molar mass. A manometer measure gas pressure and a thermometer temperature. The pressure expressed in Pascals and temperature in Kelvins. The ratio of temperature to pressure and multiply by the amount of substance of gas, and the number 8,31 the result will be the volume of the gas in m3.

# Advice 4: How to calculate building materials

In your plans overhaul or building a country house (dacha), but how much money is everything you need to know. After all, you need to calculate everything from layout to construction materials. But how to guess the quantity and price of all units know.

You will need

- project, time, money

Instruction

1

Company. Today there are many firms that for your money do all the work, since the calculation of the building materials and ending with the construction of the house. The main thing that you will need to do is tell your vision, desires and, of course, to pay the organization for services. The price can reach round the amounts, but you won't need to waste your time, effort and nerves.

2

Do it yourself. If you decide to do everything yourself and not rely on someone, there is a lot to consider. Really, so you'll save money, plus be sure that everything is done on the conscience.

3

The house project. The first thing you should do is to make a project plan of the future house. To do this, swipe the measurements of the room, which is beyond repair. Consider the maximum and minimize waste, if it is real.

4

Calculation of building materials. First calculate the cost of the so-called "draft" materials - those that are needed for preparatory works. This plaster, nails, primers, fillers, adhesives, dry mixes, plumbing pipes, wires, cranes and other. Next, calculate the cost of finishing materials. It's linoleum, parquet Board, parquet, skirting, fitted carpet, decorative coatings, ceilings, Wallpaper, decorative panels, PVC Windows, doors, electrical outlets, sanitary devices, tiles, etc.

5

During the calculation of quantity of materials such as carpet, Wallpaper, linoleum, tile measure beforehand once more the room, considering the arches, niches, over door and around the window space.

6

Purchase. Pre-take a trip to the market, visit the hypermarkets, etc. the Main goal is to find the reasonable price and promotions. At the time of purchase be sure to take a structured project plan, otherwise you can buy an extra or, worse, forget to buy something.

Useful advice

The calculation is conducted, and materials during the repair is not enough. To avoid this, after counting the cost necessarily add to the amount of 15-20 percent, and if you are planning a major overhaul, all 25%.

# Advice 5: How to calculate the volume of the barrel

Many building materials, fuel, food products, arrive at the wholesale markets in containers of cylindrical or similar to those forms. It can be barrels, tanks, or cans. In all such cases for determining the amount of a substance you first need to calculate the volume. Form of these containers may differ from the classical cylinder, and therefore methods of calculation will differ.

You will need

- - instruments for measuring length;
- calculator.

Instruction

1

The barrel may have a proper cylindrical form. In this case, its base is a circle. If possible, locate the center of the base, flick through it and measure the diameter. Divide it by 2. Get the radius. This can be done from lying on its side or inverted barrel. When this is not possible, measure the circumference of the base and find the radius by the formula R=P/2π, where R is the base radius, and P is the circumference.

2

Measure the height of the barrel. This is most easily done with a tape measure. For accuracy, draw on the side line which is strictly perpendicularly to the base. Calculate the volume of the barrel using the same formula, as the amount of any other cylinder. V=π*R2*H, where V is the volume, R is the radius of the base of the barrel, H is the height.

3

The base barrels is not necessarily a circle, and the side surface may be curved. In this case, you need to make a few more measurements. If her flanks are curved in a parabola or an arc of a circle, calculate or even measure the diameter of the middle section. Indicate the base diameter D' and the area of the middle cross-section as D".

4

The volume of the barrel, the lateral surface which is curved in an arc of a circle, calculate by multiplying the number π to 1 / 12th of the height and the sum of twice the square of the diameter of the middle section and square base. This can be expressed by the formula V=π*H/12*(2D 2+D'2), where H – height, D' and D" respectively, the diameters of the base and middle section, and V is the volume.

5

On a similar principle is calculated, and the volume of the barrel, the lateral surface which is curved in a parabola. It is equal to the product of the number π to 1/15 of the height and the sum of twice the square of the base diameter, the works of both diameters and 0, 75 square base diameter). This action may be designated by the formula V=π*H/15*(2D 2+D'*D+0,75 D'2).

Useful advice

If you need to calculate the volume is not real drums, but given in the problem, make the necessary construction. Draw the barrel itself, marking on it the given in the problem size. You must know the height of the barrel and one of the parameters of the base and middle section.

In order to better imagine the curve of a parabola or arc of a circle, use the program AutoCAD. It allows you to draw an accurate scan of the barrel, which is very easy to find options that allow you to calculate the volume.

In order to better imagine the curve of a parabola or arc of a circle, use the program AutoCAD. It allows you to draw an accurate scan of the barrel, which is very easy to find options that allow you to calculate the volume.

# Advice 6: How to calculate the volume of a cone

A cone (more precisely, a circular cone) is a solid formed by rotating a right triangle around one of its legs. Being three-dimensional body, the cone is characterized by, among other things, volume. This volume is necessary to be able to calculate.

Instruction

1

The cone can be set in different ways. For example, it may be known to the radius of its base and the length of the side. Another option is the base radius and height. Finally, another way of setting a circular cone is to specify the vertex angle and height. As is easily seen, all these methods define a circular cone by far.

2

Most often known for the base radius and the height of the cone. In this case, you must first calculate the area of the base. According to the formula of the circle it will be equal to NR^2, where R is the base radius of the cone. Then the volume of the body is equal to NR^2*h/3 where h is the height of the cone. This formula is easily checked using the integral calculus. Thus, the volume of a circular cone is exactly three times less than the volume of cylinder with same base and height.

3

If the height is not specified, and instead the known base radius and the length of the sides, to determine the amount you initially have to find the height. Since the lateral side is a hypotenuse of a right triangle, and the radius of the base serves as one of the other two sides, then the height will be the second leg of the same triangle. By the Pythagorean theorem h = √(l^2 - R^2), where l is the length of the sides of the cone. It is obvious that this formula will make sense only when l ≥ R. if l = R, then the height becomes zero, since the cone in this case turns in a circle. If l < R, the existence of such a cone impossible.

4

If you know the angle at the vertex of the cone and its height, then volume will need to find the radius of the base. To do this, you will have to refer to the geometrical definition of the cone-like body formed by rotation of a right triangle. In this known angle at the vertex is twice the corresponding angle of the triangle. Therefore, the angle at the vertex it is convenient to denote 2α. Then the angle of triangle will be equal to α.

5

By definition of the trigonometric functions of the desired radius is equal to l*sin(α), where l is the length of the sides of the cone. At the same time, known according to the problem height of the cone equal to l*cos(α). From these equalities it is easy to derive that R = h/cos(α)*sin(α) or, equivalently, R = h*tg(α). This formula always makes sense, since the angle α being an acute angle of a right triangle will always be less than 90°.

# Advice 7: How to calculate market size

The volume

**of the market**is the indicator telling you how much goods or services consumed in a geographical area per unit time. The concept of "volume"**of the market**is often confused with its "capacity", the difference being that the capacity is evidence of effective demand, the volume of really sold products or services.Instruction

1

First you need to define the geographic area described by the market (or segment) and sources of information – as a rule, the results of surveys, studies, expert opinions, statistics etc. Determine the period of time that will be (usually the month, quarter or year) and the units in which you will measure the volume

**of the market**. Can be in pieces or litres (when it comes to certain groups of goods), but rather in monetary units.2

Evaluate possible sources of information and collect in sufficient for your needs, the amount of opinions of experts, statistics, survey data. You need to find the most accurate and, most importantly, check the data. In some cases, will have to do analytical work, comparing the disparate pieces of information and bringing all data into a common format (say, in rubles). There may be a number of difficulties, for example, the amount

**of market**goods in General easier to calculate than**market**services. Also much easier to estimate the amount**of the market**or a sector in General, the volume**of the market**of a single product or (especially) services; in this case, most likely you will have to resort to methods of indirect assessment.3

The resulting "raw" data you need to present several important indicators. The first is the total volume

**of the market**in a given time interval, the dynamics of its changes in two or three preceding time interval and the forecast or trend the next. The second is the distribution of the total volume between territories, as a rule, show the share of large cities in the total volume), their dynamics and trends. The third indicator is the volume distribution**of the market**between the leading players (and therefore how varied their share in the past, what is the prognosis). The fourth – largest selling products or product groups and their share, respectively, the dynamics and prognosis. And finally, the fifth indicator (it is not necessary, because it requires a separate study, but very significant) – the ratio in the total volume**of the market**and its capacity.# Advice 8: How to calculate compression ratio

One of the parameters adjusted by the engine –

**the degree****of compression**. The value of this indicator is closely linked to power, detonation resistance, cost effectiveness and other such salient features of the engine. In view of this, it is important to calculate the compression ratio.You will need

- calculator;
- - burette;
- glass;
- sealant.

Instruction

1

The compression ratio is defined as the ratio of the full volume ofa cylinder of the internal combustion engine to the volume of the combustion chamber. Expect this figure according to the following formula: CR=(V + C)/C, where V is the working capacity of cylinder – volume of the combustion chamber.

2

To find the capacity of one cylinder, needs engine capacity (displacement) divided by the number of cylinders. For example, if the displacement four-cylinder engine is equal to 1200 cubic centimeters, the capacity of one cylinder is equal to 300 cubic centimeters.

3

The capacity of the combustion chamber is the volume that remains above the piston when the latter is at top dead center. It includes several variables: the volume of the cavity in the head, a cut (in the bottom of the piston), the volume between the upper part of the piston unit and the upper part of the cylinder Assembly while the piston in the top dead point and the volume equal to the thickness of the strip.

4

If the gasket is round, the amount equal to its thickness, determined by the formula: Vcc=[(p*D2*L)/4]/1,000, where p=3,142, where L is the thickness of the gaskets in the clamped condition (in mm), D is the diameter of the holes in the gasket (in mm). If the gasket is not round, then measure the volume at the burette. To do this, glue the gasket with sealant to the glass, then place glass on a flat surface and fill with water the hole in the gasket, using a burette.

5

Knowing the working capacity of the cylinder and the combustion chamber volume, substitute these values into the formula and calculate the compression ratio.

6

Thermal efficiency is directly related to the compression ratio: the higher the compression the less fuel used by an engine to generate the required power.

Note

In any case, do not modify independently the combustion chamber because they may interfere with the processes of displacement!

Useful advice

The efficiency of diesel engines is largely due to typical values of compression ratio: the value of this indicator may vary from 18:1 to 22:1.

# Advice 9: How to calculate the volume of the heating system

With the installation of heating devices in homes, industrial and office buildings often need to know the amount of

**system****heating**. Well, when such data are provided by the customer, but it happens not always. There are methods of assessing total**system**and its individual components, depending on capacity.Instruction

1

To calculate the volume of the heat carrier in the heating system when it replacement or reconstruction special use design tables available in reference editions. So, one section of the aluminium radiator has a volume of 0.45 liters of coolant, the section of the new iron battery – 1 L., section of old cast-iron batteries – 1.7-liter one meter pipe with a diameter of 15 mm – 0,177 l of coolant, and if used, the pipe diameter, e.g. 32 mm, the volume is 0.8 l and so on.

2

One of the most common occasions when you want to find out the amount

**of system****of heating**– the installation of the expansion tank and feed pumps. Total volume**system****heating**at the same calculate by adding the volumes of the boiler, heating devices (radiators) and piping part**of the system**by the formula:V = (VS x E) / d, where V is the volume of the expansion vessel; VS is the total volume**of the system**(boiler, radiators, pipes, heat exchangers etc); E - the coefficient of expansion of the liquid ( % ); d - efficiency of the expansion tank.3

The calculations consider such factors as the expansion of the fluid. For water systems,

**heating**it is approximately 4%. In the case of use in the system of ethylene glycol expansion coefficient of approximately 4.4 percent.4

For less accurate calculating

**system****of heating**, use a formula based on power: 1 kW = 15 HP For such approximate calculations require knowledge of the power**system****of heating**, the need for details to calculate the size of pipes, radiators, the boiler and other elements**of the system**disappears. Example: if the heating power for a residential building is 50 kW, the total volume**system****heating**VS is computed as:VS = 15 x 50 = 750 L.5

When conducting calculations keep in mind that in the case of use in the system

**of heating**and new modern radiators and pipes, the volume**of the system**would be less. Detailed information can be found in the technical documentation of the hardware manufacturer.