Instruction

1

Find out the density (ρ) of the material constituting the physical body, the volume of which you want to calculate. Density is one of the two characteristics of the object involved in the calculation formula of the volume. If we are talking about real objects, the calculations used the average density as homogenous physical body in real conditions it is difficult to imagine. It must be unevenly distributed, at least microscopic voids or inclusions of foreign material. Keep in mind when defining this setting and the temperature - the higher it is, the less the density of the material, since heat increases the distance between its molecules.

2

The second parameter, which is needed to calculate volume - mass (m) of the body. This value will be determined, as a rule, the results of the interaction of the object with other objects or created their gravitational fields. This files most often have to deal with the mass, expressed through interaction with the Earth's gravity - the weight of the body. Ways to determine this value for relatively small objects simple - they just need to weigh.

3

To calculate the volume (V) of the body divide a certain in the second step, the parameter - weight - the parameter obtained in the first step - the density: V=m/ρ.

4

In practical calculations, to the calculations it is possible to use, for example, the calculator volume. It is convenient because does not require to look somewhere else the density of the desired material and enter it into a computer in the form there is a dropdown list with a list of the most frequently used in calculations of materials. Clicking the desired line, enter in the "Weight" weight, and in the "calculation Precision" set the number of decimal places that should be present in the calculations. The volume in liters and cubic meters you'll find in placed below the table. There just in case you will be given the radius of the sphere and the side of the cube, which should correspond to this volume of selected substances.

# Advice 2 : How to find the edge of the cube

Knowing some parameters of the cube, you can easily find it edge. It is enough just to have information on its volume, face area, or the length of the diagonal of a face or cube.

You will need

- Calculator

Instruction

1

Basically, there are four types of tasks that you need to find the edge of the cube. This definition of the length of the cube edges of the square faces of a cube, volume of a cube diagonal of the cube face diagonal of the cube. Consider all four options such tasks. (The rest of the task tend to be variations of the above or a task in trigonometry, having a very indirect relation to the subject)

If famous square faces of a cube, find the edge of the cube is very simple. As the face of the cube is a square with a side equal to the edge of the cube, its area equals the square of the cube. Hence the edge length of the cube equals the square root of the square of its faces, ie:

a=√S, where

a - the edge length of the cube

S - square face of the cube.

If famous square faces of a cube, find the edge of the cube is very simple. As the face of the cube is a square with a side equal to the edge of the cube, its area equals the square of the cube. Hence the edge length of the cube equals the square root of the square of its faces, ie:

a=√S, where

a - the edge length of the cube

S - square face of the cube.

2

Finding the face of the cube by its volume even easier. Given that the volume of a cube equals the cube (third-degree) length of the cube, we get that the edge length of the cube equals the cube root (third-degree) from its scope, ie:

a=√V (cube root), where

a - the edge length of the cube

V is the volume of the cube.

a=√V (cube root), where

a - the edge length of the cube

V is the volume of the cube.

3

A little harder to find the length of the edges of the cube according to the known lengths of the diagonals. We denote by:

a - the edge length of the cube;

b - the length of the diagonal of the cube face;

c - the length of the diagonal of the cube.

As can be seen from the figure, the diagonal face and edges of the cube form a rectangular equilateral triangle. Therefore, by the Pythagorean theorem:

a^2+a^2=b^2

(^ - icon exponentiation).

Hence, we find:

a=√(b^2/2)

(to find the edge of the cube to extract the square root of half the square of the diagonal faces).

a - the edge length of the cube;

b - the length of the diagonal of the cube face;

c - the length of the diagonal of the cube.

As can be seen from the figure, the diagonal face and edges of the cube form a rectangular equilateral triangle. Therefore, by the Pythagorean theorem:

a^2+a^2=b^2

(^ - icon exponentiation).

Hence, we find:

a=√(b^2/2)

(to find the edge of the cube to extract the square root of half the square of the diagonal faces).

4

To find the edge of the cube its diagonal, again use a picture. The diagonal of a cube (C) diagonal edge (b) and the edge of the cube (a) form a rectangular triangle. So according to the Pythagorean theorem:

a^2+b^2=c^2.

Use vyshesteblievskoy dependence between a and b and substitute into the formula

b^2=a^2+a^2. Received:

a^2+a^2+a^2=c^2, where we find:

3*a^2=c^2, therefore:

a=√(c^2/3).

a^2+b^2=c^2.

Use vyshesteblievskoy dependence between a and b and substitute into the formula

b^2=a^2+a^2. Received:

a^2+a^2+a^2=c^2, where we find:

3*a^2=c^2, therefore:

a=√(c^2/3).

# Advice 3 : How to find the area and volume of a cube

A cube is a rectangular parallelepiped of which all edges are equal. Therefore, the General formula for the volume of the rectangular prism and the formula for its surface area in the case of

**Cuba**easier. The volume**of a cube**and**the area of**the surface can be found, knowing the volume of a sphere inscribed in it, or sphere, described around it.You will need

- the length of a side of a cube, the radius of the inscribed and circumscribed ball

Instruction

1

The volume of a box is: V = abc, where a, b, c is its dimension. Therefore, the volume

**of a cube**is equal to V = a*a*a = a^3, where a is the side length**of the cube**.The surface area of**a cube**is equal to the sum of the areas of all its faces. Only**the cube**has six faces, so**the area of**its surface equal to S = 6*(a^2).2

Let the ball inscribed in the cube. Obviously, the diameter of the ball is equal to the side

**of the cube**. Substituting the length of the diameter in the expression for the volume instead of the length of the edges**of the cube**and using that the diameter is twice the radius, then get V = d*d*d = 2r*2r*2r = 8*(r^3) where d is the diameter of the inscribed circle, and r is the radius of the inscribed circle.The surface area of**the cube**will then be equal to S = 6*(d^2) = 24*(r^2).3

Let the ball circumscribed around

Consider first one of the faces

**the cube**. Then its diameter will coincide with the diagonal**of the cube**. The diagonal**of the cube**passes through the center**of the cube**and connects two opposite points.Consider first one of the faces

**of the cube**. The edges of this face are the legs of a right triangle in which the face diagonal d is the hypotenuse. Then by the Pythagorean theorem we get: d = sqrt((a^2)+(a^2)) = sqrt(2)*a.4

Then consider the triangle in which the hypotenuse is the diagonal

So, derived the formula of diagonal

**of a cube**and the diagonal edge of d and one edge**of cube**a to his legs. Similarly, by the Pythagorean theorem we get: D = sqrt((d^2)+(a^2)) = sqrt(2*(a^2)+(a^2)) = a*sqrt(3).So, derived the formula of diagonal

**of a cube**is equal to D = a*sqrt(3). Hence, a = D/sqrt(3) = 2R/sqrt(3). Therefore, V = 8*(R^3)/(3*sqrt(3)), where R is the radius of the ball is described.The surface area of**a cube**is equal to S = 6*((D/sqrt(3))^2) = 6*(D^2)/3 = 2*(D^2) = 8*(R^2).# Advice 4 : How to find the mass, knowing the density

In physical and practical challenges often encountered such quantities as mass,

**density**and volume. Of course, to find the**mass**, knowing the density, you must know the volume of a body or substance. However, sometimes the volume of the object is unknown. In such cases it is necessary to use indirect data or to measure the volume yourself.You will need

- a calculator or computer, a ruler, tape measure, measuring device

Instruction

1

To find the mass , knowing the density, divide the volume of a body or substance to its density. That is, use the formula: m = V / ρ where:V – volume,

ρ is the density,

V is the volume.Before the calculation of the mass bring all units into one system, for example, in the international system of measurement (SI). To do this, turn the volume in cubic meters (m3) and the density in kilograms per cubic meter (kg/m3). In this case, the value of the mass obtained in kilograms.

ρ is the density,

V is the volume.Before the calculation of the mass bring all units into one system, for example, in the international system of measurement (SI). To do this, turn the volume in cubic meters (m3) and the density in kilograms per cubic meter (kg/m3). In this case, the value of the mass obtained in kilograms.

2

If density and volume are given in one system of units, then pre-translate in C to produce optional. The mass of a body or substance in this case is measured in the unit of mass that is indicated in the numerator of the density units (units of volume in the calculation will be reduced).

For example, if the volume is specified in liters, and the density in grams per liter, the calculated weight obtained in grams.

For example, if the volume is specified in liters, and the density in grams per liter, the calculated weight obtained in grams.

3

If the volume of the body (substances of) unknown or not specified clearly in the conditions of the problem, then try to measure, calculate or learn using indirect (secondary) data.

If the substance is granular or liquid, it typically is in the tank, which usually has a standard size. For example, the volume of the barrel is usually equal to 200 liters, the volume of the bucket is 10 liters, the volume of glass – 200 ml (0.2 liters), the volume of a tablespoon is 20 ml, the amount of a teaspoon – 5 ml. On the volume of three-liter and one-liter jars you might guess from their names.

If the liquid is not the entire capacity or the capacity of the non-standard, then pour it into another container, whose volume is known.

If a suitable container, pour the liquid using measuring cups (cans, bottles). In the process of skimming liquids just count the number of cups and multiply by the volume measuring containers.

If the substance is granular or liquid, it typically is in the tank, which usually has a standard size. For example, the volume of the barrel is usually equal to 200 liters, the volume of the bucket is 10 liters, the volume of glass – 200 ml (0.2 liters), the volume of a tablespoon is 20 ml, the amount of a teaspoon – 5 ml. On the volume of three-liter and one-liter jars you might guess from their names.

If the liquid is not the entire capacity or the capacity of the non-standard, then pour it into another container, whose volume is known.

If a suitable container, pour the liquid using measuring cups (cans, bottles). In the process of skimming liquids just count the number of cups and multiply by the volume measuring containers.

4

If the body has a simple shape, then calculate its volume using the appropriate geometric formula. For example, if the body has the shape of a rectangular parallelepiped, then its volume will be equal to the product of the lengths of its edges. That is:V [PR].couples. = a*b*c where:V [PR].couples. – the volume of a rectangular parallelepiped, and

a, b, c - values of its length, width and height (thickness), respectively.

a, b, c - values of its length, width and height (thickness), respectively.

5

If the body has a complex geometric form, then try the (relatively!) break it down into a few simple parts, find the volume of each of them separately and then add up the resulting values.

6

If the body cannot be divided into more simple shapes (e.g., a statue), then use the method of Archimedes. Lower the body into the water and measure the volume of displaced fluid. If the body does not sink, then "push" it with a thin rod (wire).

If the volume of the displaced body of water is problematic to calculate, then weigh the resulting water, or find the difference between initial and remaining mass of water. At the same time, the number of kilograms of water will equal the number of liters, the number of grams of the number of milliliters, and the number of tons quantity cubic meters.

If the volume of the displaced body of water is problematic to calculate, then weigh the resulting water, or find the difference between initial and remaining mass of water. At the same time, the number of kilograms of water will equal the number of liters, the number of grams of the number of milliliters, and the number of tons quantity cubic meters.

# Advice 5 : How to find side of a cube

The cube is one of the simplest three-dimensional shapes. It consists of six perpendicular faces, representing equal squares. The line of intersection of faces

**of a cube**are its edges, and the intersection points of edges are vertices. Sometimes you can hear a "term" as the "face"**of the cube**. Depending on the specific situation, this term may be implied as a face**of a cube**and its edge.In life and games (if you are using cube as a dice) a side of**a cube**is usually called its faces. If you find**the side of****Cuba**trying student, you probably need to determine the length of his ribs (**the cube**, not the student).You will need

- calculator

Instruction

1

The cube is so symmetrical figure that in order to find his side (rib) enough to know at least one of the main parameters

P - square faces

**of the cube**. These include its volume, area of facets, length of the diagonal faces and the length of the diagonal**of the cube**(so-called "big diagonal").To find**side****of a cube**if you know the area of one side, remove from the numeric value of the square faces of the square root. As a formula, this relationship can be written in the following form:S = √P where: – length of sides (faces)**of the cube**,P - square faces

**of the cube**.This formula is derived from the fact that the face**of the cube**is a square with a side equal to the edge**of the cube**and square equal to the square of the ribs.2

Finding the sides (edges)

(3√ - the function of extracting the cube root).

**of a cube**, given the volume similarly. As the volume**of a cube**is equal to the third order (cube) of the lengths of its edges, to determine the length of the edges**of the cube**remove from its scope the cube root. That is, use the formula:S = 3√V, where the volume**of the cube**.(3√ - the function of extracting the cube root).

3

To find the sides (edges)

**of the cube**diagonal of its faces, extract the square root of the square of the diagonal divided by two. As a formula this rule as follows:S = √(D2/2), where d is the length of the diagonal faces**of the cube**. The validity of this formula follows from the Pythagorean theorem because the diagonal and two adjacent edges form an equilateral right triangle, where the diagonal is the hypotenuse, and the edges of the legs.4

To find the

**side**(edge)**of the cube**on its diagonal (which is the diagonal**of the cube**and not the faces) and extract the square root of one third of the square of the length of this diagonal. That is, use the same previous formula:S = √(L^2/3).This formula is also derived based on the Pythagorean theorem because the diagonal**of the cube**, the diagonal edge and the edge**of the cube**form a rectangular (but longer shaft than crossbar) triangle.Useful advice

For finding square roots and cube roots use a scientific calculator. To extract the root of the third degree raise to the power of⅓.

# Advice 6 : How to find mass of a cube

Sometimes in practice and in solving school problems you want to find the mass of the cube. To give the correct answer to this question needs first to be clarified: what is meant by "cube". Students usually have to find the mass of this cube, sometimes quite large. In everyday life, under the weight of a cube usually involve the mass of one cubic meter of a substance.

You will need

- calculator, table of density of a substance.

Instruction

1

To find the mass of the cube as a physical body, measure the edge length of the cube and determine the density of matter, which consists of cubic edge Length of a cube record in meters (m), and the density in kilograms per cubic meter (kg/m3). To determine density, use the appropriate tables of the density of a substance. If the density of the substance expressed in g/cm3, then transfer to kg/m3 multiply this number by 1000. Then multiply the density of matter on the Dean of the cube erected in the third degree. That is, use the formula:

M = N * P3,

where:

M – mass of the cube in kilograms,

P is the density of the cube in kg/m3,

R is the edge length of the cube in meters.

M = N * P3,

where:

M – mass of the cube in kilograms,

P is the density of the cube in kg/m3,

R is the edge length of the cube in meters.

2

Example.

What mass will have an ice cube size of 1 cm?

Solution.

Find in the table the substance density: the density of ice is equal of 0.917 g/cm3. Translate the density and size of the cube in the system of SI units:

1cm=0.01 m,

Of 0.917 g/cm3=917 kg/m3.

Substitute numbers into the formula, we get:

M = 917 * 0,013 = 0,000917 (kg).

What mass will have an ice cube size of 1 cm?

Solution.

Find in the table the substance density: the density of ice is equal of 0.917 g/cm3. Translate the density and size of the cube in the system of SI units:

1cm=0.01 m,

Of 0.917 g/cm3=917 kg/m3.

Substitute numbers into the formula, we get:

M = 917 * 0,013 = 0,000917 (kg).

3

If the size of the cube is unknown and difficult to measure, then determine the volume of the cube. To do this, place the cube in a measuring vessel with water and determine the volume of liquid displaced by it.

Alternatively, it is possible to determine the mass of the displaced water cube. The mass of the displaced water in grams, multiplied by 1000000 will equal the volume of cube in m3.

After determining the volume of the cube and its density, find its mass using the following formula:

M = P * V,

where: V is a classical designation of the volume.

Alternatively, it is possible to determine the mass of the displaced water cube. The mass of the displaced water in grams, multiplied by 1000000 will equal the volume of cube in m3.

After determining the volume of the cube and its density, find its mass using the following formula:

M = P * V,

where: V is a classical designation of the volume.

4

If you just need to find the mass of the cube, then, apparently, means the mass of a cubic meter of any substance. It may be fluid, granular substance or material (e.g., boards). To determine the mass of a cube in this case, just specify the density of the substance. The numerical value of the density, expressed in kg/m3, and is the mass of the cube in kilograms. In this case, note that the density of water and weak aqueous solutions is equal to 1000 kg/m3, i.e., the mass of a cube of water is equal to 1000 kg (one ton).

# Advice 7 : How to find the mass of the square

Sometimes web requests are staggering: how to find

**the mass**or volume of a triangle,**square**or circle. The answer is no. Square, triangle, etc. – flat shapes, the calculation of mass and volume may only have three-dimensional shapes. And under the square could be a cube or a parallelepiped, one of whose sides is a square. Knowing the parameters of these shapes, you can find the volume and**mass**.Instruction

1

To calculate the volume of a cube or cuboid you need to know three values: length, width and height. To calculate the mass required volume and density of the material of the object (m = v*ρ). The density of gases, liquids, rocks, etc. can be found in the relevant tables.

2

Example 1. Find the

**mass**of a granite block, whose length is 7 m, width and height 3 m. the Volume of such a parallelepiped will be equal to V = l*d*h, V = 7m*3M*3M = 63 m3. The density of granite is 2.6 t/m3. The mass of the granite block: 2.6 t/m3 * 63 m3 = 163,8 T. a: 163,8 tonnes.3

You need to consider that the sample may not be uniform or may contain impurities. In this case, you will need not only the density of the base material, but the density of impurities.

4

Example 2. Find the

**mass**of a cube with sides 6 cm, which consists of 70% pine and 30% spruce. The volume of a cube with a side l = 6 cm is 216 cm3 (V=l*l*l). The volume that is occupied in the specimen pine, can be calculated using a proportion:216 cm3 - 100% X – 70%; X = 151,2 cm35

The volume that is occupied by spruce: 216 cm3 - cm3 151,2 = 64,8 cm3. Pine density of 0.52 g/cm3, so the mass of pines, contained in the sample of 0.52 g/cm3*cm3 151,2 = 78,624 g ate Density of 0.45 g/cm3, respectively - the mass is equal to 0.45 g/cm3*64,8 cm3 = amounted to 29.16 g. Answer: the total mass of the sample, consisting of spruce and pine 78,624 g + amounted to 29.16 g = 107,784 g

6

And even if you need to calculate

**the mass of**a square sheet metal, then you will calculate**the mass**of the parallelepiped whose length l, width d and height (sheet thickness) h.7

Example 3. Find

**the mass of**copper square sheet, 10 cm by 10 cm, thickness 0,02 see the Density of copper 89,6 g/cm3. The volume of copper sheet: 10 cm*10 cm*0.02 cm = 2 cm3. m(sheet) = 2 cm3*89,6 g/cm3 = 179,2 g Answer: the mass of the sheet - 179,2 g.Note

In metal, there is the concept of mass of a square. This refers to the mass of calibrated metal rod with a square cross-section. But, regardless of how "this" is, in fact, this rod is still the same box.