Instruction

1

The conditions of the problem when finding the diagonal axial

**section****of the cylinder**may be different. Carefully read the text of a task, select the known data.2

The base radius and height

**of a cylinder**If your problem is known to such factors as the radius**of the cylinder**and its height, then based on this, find the*diagonal*. Since the axial section is a rectangle with sides that equal the height**of the cylinder**and the diameter at the base, then*diagonal***sections**- is the hypotenuse of right triangles forming the axial section. The legs in this case are the base radius and height**of the cylinder**. By the Pythagorean theorem (c2 = a2 + b2) find*the diagonal*axis**of the cross section**:D = √〖(4R〗^2+H^2) where D is*the diagonal*axial**section****of the cylinder**, R is the base radius, H – height**of the cylinder**.3

The base diameter and the height

**of the cylinder**If the task of the diameter and height**of cylinder**are equal, then in front of you is an axial section in the form of a square, the only difference of this condition from the previous in that you will need to split into 2 base diameter. Continue to act in accordance with the Pythagorean theorem, as in the previous problem.4

The height and the surface area

**of a cylinder**Read carefully the conditions of the problem, with a known height and area must be the hidden data, for example, the caveat that the height is greater than the base radius 8 cm In this case, find the radius of this square, then use the radius calculate height, then the Pythagorean theorem – the diameter of the axial**section**:Sp = 2πRH+2nr^2 , where Sp is the surface area**of the cylinder**.Print out the formula for finding the height using the surface area**of a cylinder**, remember that the condition H = 8R.H = (Sp - 2nr^2) / 2nr.Useful advice

Depicting a drawing on paper, try to use as much of the sheet size for the image cylinder. Than stronger and bigger the drawing, the will be presented the solution to the problem.

# Advice 2: How to find the diagonal

Each polyhedron, a rectangle, a parallelogram and a

**diagonal**. It usually connects the corners of any of these geometric shapes. The value of the diagonal has to find the solution of problems in elementary and higher mathematics.Instruction

1

**A diagonal**is any straight line connecting the corners of the polyhedra. Its location depends on the type of shapes (rhombus, square, parallelogram) and the data given in the problem. The easiest way to find the diagonal of a rectangle is the following.The two sides of the rectangle a and b. Knowing that all of its angles equal to 90°, and its

**diagonal**is the hypotenuse of the two triangles, we can conclude that

**the diagonal of**this fighti can be found by using the Pythagorean theorem. In this case, the sides of the rectangle are the legs of triangles. It follows that

**the diagonal**of a rectangle is:d=√(a^2+b^2)a special case of applying this method to finding diagonals is a square. Its

**diagonal**can also be found by the Pythagorean theorem, but given that all its sides are equal,

**the diagonal**of a square is equal to a√2. The value a is the square side.

2

If given a parallelogram, its

arambam is called a parallelogram whose all sides are equal. Let him have the two sides equal to a, and, the unknown

**diagonal**find, as a rule, cosine theorem. However, in exceptional cases, for a given value of the second diagonal can be found from the first equation:d1=√2(a^2+b^2)-d2^2Теорема of cosines applies when not given a second**diagonal**and are given only the sides and corners. It is a generalized Pythagorean theorem. For example, given a parallelogram whose sides are b and c. Through two opposite corners of a parallelogram is**the diagonal of**a. Since a, b and c form a triangle, we can apply the theorem of cosines, which can be computed**diagonal**:a^2=√b^2+c^2-2bc*cosα When given the area of a parallelogram and one of the*diagonals*, and the angle between the two diagonals, the**diagonal**can be calculated in the following way:d2=S/d1*cosarambam is called a parallelogram whose all sides are equal. Let him have the two sides equal to a, and, the unknown

**diagonal**. Then, knowing the theorem of cosines,**the diagonal**can be calculated by the formula:d=a^2+a^2-2a*a*cosα=2a^2(1-cosα)3

The diagonal of a trapezoid is several ways. To calculate you need to know, as a rule, three values - top and bottom base, and at least one lateral side. This can be seen on the example of a rectangular trapezoid.For example, given a rectangular trapezoid. First you need to find a small segment that is a leg of a right triangle. It is equal to the difference between the upper and lower bases. As a rectangular trapezoid, the drawing shows that the height is equal to the side of the trapezoid. As a result, you can find another lateral side of the trapezoid. If you know the upper base and lateral side, the cosine theorem can be found first

**diagonal**:c^2=a^2+b^2-2ab*soavtory**diagonal**is based on values of the first lateral side and the upper base on the Pythagorean theorem. In this case, this**diagonal**is the hypotenuse of a right triangle.# Advice 3: How to determine the size of cable diameter

As a rule, any cable consists of several cores which in cross section present you round. It is from the area of the cross section proportional to the conductivity of the cable. If it is too small, the cable may burn out, and this is one of the main causes of fires in the modern world.

You will need

- cable with an unknown cross section;
- - Vernier caliper or micrometer;
- - table of specific resistances of substances.

Instruction

1

Take the cable, the section which you want to define. Most often it consists of 2-4 lived that are isolated from each other special material. These cores have the same diameter. Sometimes you can find the cable alone which is thinner than the rest – it is meant for grounding.

2

Clean off the insulation of the cable core. With the help of Vernier caliper and micrometer better (this will allow for more accurate measurement), find the diameter of the core. Get the value in millimeters. Then calculate the cross-sectional area. To do this, a coefficient of 0.25 and multiply by the number π≈3.14, and the value of the diameter d squared S=0,25∙π∙d2. This value multiply by the number of strands of the cable. Knowing the wire length, its cross section and the material from which it is made, and calculate the resistance.

3

For example, if you need to find a cross-section of copper cable of 4 lived, and the measurement of the diameter gave a value of 2 mm, find the area of its cross section. To do this, calculate the cross-sectional area of one core. It will be equal to S=0.25∙3,14∙22=3,14 mm2. Then determine the total cross section of the cable for this section one core to multiply their number in our example is 3,14∙4=12,56 mm2.

4

You can now determine the maximum current that can be it leaking, or resistance if known length. Maximum current for copper cable, calculate the ratio of 8 to 1 mm2. Then the limit value of current which can pass through the cable, taken in the example is 8∙12,56=100,5 A. Note that for aluminum cable, the ratio is 5 to 1 mm2.

5

For example, the cable length is 200 m. in order to find its resistance, multiply resistivity of copper ρ in Ohm∙ mm2/m, the cable length l and divide by the area of its cross section S (R=ρ∙l/S). Making the substitution, we get R=0,0175∙200/12,56≈0,279 Ohms, which will lead to very small losses of electricity during its transmission through such a cable.

# Advice 4: How to find the volume of a cylinder

Cylinder refers to three-dimensional geometric shapes, the so-called solids of revolution. Its bases are equal circles. The cylinder can be straight and inclined.

You will need

- — the range;
- calculator.

Instruction

1

In that case, if you know the area of at least one of the bases

**of the cylinder**(they are equal), measure its height. To do this, drop a perpendicular from one base**cylinder**on to another, and measure its length. The height of the straight**cylinder**is equal to any of the sides. Then find the volume by multiplying the area of one of the bases**of the cylinder**S to the height h (V=S∙h). For example, if you know that the area of the circle lying at the base**of the cylinder**is 8 cm2 and its height is 5 cm, then its volume is V=8∙5=40 cm3.2

In that case, if the base area of

**the cylinder**is unknown, its volume can be found using another formula. Measure the height**of the cylinder**in any convenient way. Then, find the diameter of the base**of the cylinder**by measuring its convenient way, for example, using a ruler or calipers. Calculate the radius**of the cylinder**by dividing the diameter by 2. Find the volume of this geometric body by multiplying the number π≈3,14 the square of the radius R and the height**of the cylinder**h (V= π∙R2∙h).3

Example.Find the volume

**of a cylinder**, whose base has a diameter of 6 cm and the height is 5 cm Determine the base radius**of the cylinder**R=6/2=3 cm Calculate the volume V= 3,14∙32∙5=141,3 cm3.4

If the cylinder is inclined, the above formula remains valid, but the height in this case is not equal to the generatrix. Therefore, in order to find the volume, measure the length of the generatrix l, and multiply it by the area of the base S, which can be found as described above, and the sine of the angle α between the generatrix and the plane of the base V=S∙l∙sin(α).

5

Example. Forming a circular

**cylinder**has a length of 16 cm and is at an angle of 45 ° to the base. Find the volume**of a cylinder**if the base radius is 8 cm First, find the area of the base**of the cylinder**. It is equal to S=π∙R2. Substitute the value of this formula in the expression for the volume and get V= π∙R2∙l∙sin(α)=3,14∙82∙16∙sin(45°)≈2273,6 cm3.# Advice 5: How to find the area of an axial section of a truncated cone

To solve this problem, it is necessary to remember that such a truncated cone and which properties it possesses. Be sure to make a drawing. This will allow you to determine what geometric figure represents a cross section

**of a cone**. It is possible that after the solution of the problem will not be present for you difficulty.Instruction

1

A round cone is the body obtained by rotating a triangle around one of its legs. Direct, outbound from the vertex

**of the cone**and intersecting the base, called forming. If all the generators are equal, then the cone is straight. At the base of a circular**cone**is the circle. The perpendicular on the base from the top, is the height**of the cone**. Have a round straight**cone**height coincides with its axis. The axis is the line connecting the vertex with the centre of the base. If horizontal clipping plane of a circular**cone**parallel to the base, its upper base is a circle.2

Because the clause is not specified what kind of cone is given in this case, we can conclude that this is a straight circular truncated cone, horizontal section which is parallel to the base. Its axial cross-section, i.e. a vertical plane which passes through the axis of the circular truncated

**cone**, is ravnovesnoi trapeze. All of the axial**cross section**of a round straight**cone**are equal. Therefore, in order to find*the area of the*axial**cross-section**, it is required to find*the area*of a trapezoid, bases of which are the diameters of the bases of the truncated**cone**and the side of his form. The height of the truncated**cone**is both the height of the trapezoid.3

Area of a trapezoid is given by:S = ½(a+b) h, where S is

*the area*of the trapezoid;a is the value of the lower bases of the trapezoid;b – the value of its upper base;h = height of the trapezoid.4

Because the condition is not specified, what values this can be considered that the diameters of the two bases and the height of the truncated

**cone**are known: AD = d1 – the diameter of the lower base of the truncated**cone**;BC = d2 is the diameter of its upper base; EH = h1 – the height**of the cone**.Thus,*the area of the*axial**cross-section**of the truncated**cone**is determined by: S1 = ½ (d1+d2) h1# Advice 6: How to find a life-size section

Properties of figures in space involved in this section of geometry, as geometry of space. The basic method for solving problems in solid geometry is a method of

**cross-section**polyhedra. It allows you to correctly build the**cross-section**of the polyhedra and to determine the species of these sections.Instruction

1

The definition of the

**cross-section**of any shape, that is, the actual size of this**cross-section**, often assumed in formulating the tasks of building a sloping**section**. The oblique section should be called front-secant projective plane. And build it life-size enough to perform several actions.2

With a ruler and pencil, draw in figure 3 the projections – front view, top view and side view. The main projection in the front view show the path that is front-projecting section plane, draw a sloping line.

3

On an incline direct select main points: points of entry

**section**and exit**section**. If a figure is a rectangle, the points of entry and exit will be one. If a figure is a prism, then the number of points is doubled. Two points define the entry into and figure out. The other two identify points on the sides of the prism.4

At an arbitrary distance guide line parallel to the front projecting section plane. Then, from the points located on the axis of the main view, swipe to the auxiliary line perpendicular to the inclined straight line until they intersect with the parallel axis. Thus you will get the projection of the points of the shape in the new coordinate system.

5

To determine the width of the figure, lower straight from the main point of view the figure of top view. Indicate the appropriate indices of the projection points at each intersection of a line and a shape. For example, if point a belongs to the mind of the figure the points A’ and A” belong to projective planes.

6

Put in the new coordinate system the distance that is formed between the vertical projections of the main points. The figure, which is obtained as the result of development, and is a natural value of the inclined

**section**.# Advice 7: How to translate the section in diameter

In normative documents on the design grid to indicate wire size, and caliper can measure only

**the diameter of the**core. These values are interlinked and can be translated one into another.Instruction

1

To translate specified in the statutes

**section of**a solid wire in its diameter, use the following formula:D=2sqrt(S/π), where D - diameter, mm; S - conductor cross-section, mm2 (square millimeters it electricians abbreviated as "squares").2

Flexible stranded wire consists of many thin of strands, twisted together and placed in a common insulating sheath. This allows him to survive the frequent movements of the load, which is connected with its help to the power source. To find the diameter of one conductor of the conductor (which can be measured with a Vernier caliper), first locate the cross-section of the conductor:s=S/n where s is the cross - section of one core, mm2; S is the total conductor cross-section (as specified in the regulations); n is the number of cores.Then move the cross-section of cores in diameter, as described above.

3

On printed circuit boards are used in flat conductors. Instead of diameter, they have a thickness and width. The first value is known in advance from the technical data of foil material. Knowing this, it is possible to find the width of the cross section. To do this, use the following formula:W=S/h, where W is conductor width, mm; S - conductor cross-section, mm2; h - thickness of conductor, mm.

4

The conductors are of square section are relatively rare. Its cross section must be translated to either the side length or the diagonal of a square (a caliper can measure both). The length of the side is calculated as follows:L=sqrt(S), where L is the side length, mm; S - conductor cross-section, mm2.Then the length of the sides to find the diagonal, make the following calculation:d=sqrt(2(L^2)) where d is the diagonal of a square, mm; L - length, mm.

5

If the conductor cross-section which corresponds exactly to the desired will not have, use another that has more, but in any case not smaller section. The type of conductor and its insulation you choose depending on conditions of use.

Note

Before measurement of the conductor caliper remove the supply voltage and make sure it is no using a voltmeter.

# Advice 8: How to find the diagonal of the TV

**Diagonal**

**of the TV**is useful to know. About it will ask the repair centre if the unit will need resuscitation. Given diagonal it is necessary to choose the distance at which you can sit in front of the screen.

You will need

- TV
- centimeter/roulette
- calculator
- - manual
- - Notepad and pen

Instruction

1

To know the diagonal of your TV, you can use several ways. The first and most basic is to look in the instructions to the apparatus or even on the box. Right on the cover of the user's guide specified the brand of TV, model and its diagonal.

2

It happens that neither the box nor the instructions can not be found. In this case, accurately determine what TV presented to measure: CRT (TV CRT), LCD (LCD) or plasma.

3

If you have a CRT TV, then measure the diagonal it is necessary for the glass of the bulb. Just pull the cm from one corner diagonally to another. Record the result in centimeters.

4

LCD/plasma TV before measurement it is necessary to include. Get away from him a meter and a half, look fix extreme luminous pixels in the corners. The fact that LCD and plasma TVs, the image is enclosed in a small black frame around the perimeter of the TV. So the measurements should be carried out at the most distant from each other pixels.

5

Turning off the TV, walk up to him. Apply cm from one extreme of a luminous pixel diagonally through the screen to the other. Write down the result.

6

Produce the calculations. Diagonal TV or monitor is always stated in inches. To know the right size, divide the centimeters by 2.54 see the data the result will be the diagonal of your TV.

Note

If you measure the diagonal of the TV with a tape, don't put it close to the screen. The metal can scratch the coating.

Useful advice

To accurately measure the diagonal of the TV difficult enough, so don't be surprised if you get strange number. For the reliability of the result, round it up or down.