Instruction

1

For all figures there is such a term as the height. Height is usually called the measured value of any of the figures in an upright position. The cylinder height is the line perpendicular to the two parallel bases. He also has forms. Forming a cylinder is a line, rotation in a cylinder. She, in contrast to forming other shapes, such as cone has the same height.

Consider the formula, which can be used to find the height:

V=NR^2*H where R is the base radius of a cylinder H - the desired height.

If instead of the radius given the diameter, the formula is modified as follows:

V=NR^2*H=1/4πD^2*H

Accordingly, the height of the cylinder is equal to:

H=V/NR^2=4V/D^2

Consider the formula, which can be used to find the height:

V=NR^2*H where R is the base radius of a cylinder H - the desired height.

If instead of the radius given the diameter, the formula is modified as follows:

V=NR^2*H=1/4πD^2*H

Accordingly, the height of the cylinder is equal to:

H=V/NR^2=4V/D^2

2

Also the height can be determined based on the diameter and area of the cylinder. There is a side area and the surface area of the cylinder. Part of the surface of the cylinder bounded by a cylindrical surface, called the lateral surface of the cylinder. The surface area of a cylinder includes the area of its bases.

The lateral surface area of a cylinder is calculated by the following formula:

S=2πRH

Transforming this expression, find the height:

H=S/2nr

If given the surface area of a cylinder, calculate the height in a different way. The surface area of a cylinder is equal to:

S=2nr(H+R)

First, convert the given formula as shown below:

S=2πRH+2nr

Then find the height:

H=S-2nr/2nr

The lateral surface area of a cylinder is calculated by the following formula:

S=2πRH

Transforming this expression, find the height:

H=S/2nr

If given the surface area of a cylinder, calculate the height in a different way. The surface area of a cylinder is equal to:

S=2nr(H+R)

First, convert the given formula as shown below:

S=2πRH+2nr

Then find the height:

H=S-2nr/2nr

3

Through the cylinder can hold a rectangular cross section. Width of this cross section is the same as the diameters of the bases, and the length - form shapes, which are equal to the height. If you hold through this section of diagonal, you can easily notice that a right triangle is formed. In this case, the diagonal is the hypotenuse of the triangle, leg diameter, and a second side and a height of the cylinder. Then the height can be found by using the Pythagorean theorem:

b^2 =sqrt (c^2-a^2)

b^2 =sqrt (c^2-a^2)

# Advice 2 : How to find the volume of a cylinder

A cylinder is called a geometric solid formed by a cylindrical surface bounded by two parallel planes. The cylinder obtained by rotating a rectangle around any of its sides is called a straight. With just a few simple methods you can quite accurately find the volume of a cylinder.

You will need

- • Ruler or tape measure.
- • A pencil or marker.
- • A sheet of paper or cardboard or other suitable object with right angles.

Instruction

1

Suppose you have a water tank of cylindrical shape. You need to fill it with water, but you want to calculate the volume that it will fill.

From the school course of geometry you know that the formula of volume of cylinder is:

V = SH ,

that means, the volume of a cylinder equals the area of S is at its height H.

The height of the cylinder H to easily measure a tape measure or ruler.

From the school course of geometry you know that the formula of volume of cylinder is:

V = SH ,

that means, the volume of a cylinder equals the area of S is at its height H.

The height of the cylinder H to easily measure a tape measure or ruler.

2

Now, define the footprint. The area of a circle, as we know from school the geometry is determined by the formula:

S = πR2,

where π is the digit in mathematics the ratio of the lengths of the circumference and the diameter and is equal to 3.14159265...,

and R is the radius of the circle

How to calculate the area of a circle with only a ruler? Very simple!

From the same school course of geometry recall that any circle can be inscribed right triangle. Moreover, the hypotenuse of this triangle is equal to the diameter of the circle.

To do this, take a piece of cardboard or other suitable object having angles and imposed on our cylinder so that a right angle α with its tip And rests against the edge of the cylinder.

S = πR2,

where π is the digit in mathematics the ratio of the lengths of the circumference and the diameter and is equal to 3.14159265...,

and R is the radius of the circle

How to calculate the area of a circle with only a ruler? Very simple!

From the same school course of geometry recall that any circle can be inscribed right triangle. Moreover, the hypotenuse of this triangle is equal to the diameter of the circle.

To do this, take a piece of cardboard or other suitable object having angles and imposed on our cylinder so that a right angle α with its tip And rests against the edge of the cylinder.

3

Side of the rectangle that are intersected by the circle, mark it with a pencil or marker and connect with a straight line. In our case, the vertices of the triangle b and C. This cut is the diameter of our circle. The radius of the circle is equal to half its diameter. Divide the segment BC into two parts. The center of the circle is point O. the Segments Ob and OC are equal and are the base radius of the cylinder. Now substitute the obtained values into the formula:

V = πR2H

V = πR2H

Note

If you can measure the parameters of your cylinder in inches, the result will be in cubic centimeters (cm3). If the measurements are taken in metres, the result will be, respectively, obtained in cubic metres (m3).

Useful advice

If you must convert cubic inches to liters of volume, then multiply the result by 0, 001, this is the volume of the cylinder in litres. If your result will be calculated in cubic meters, then multiply it by 1000. For example: you got in the result of measurements and calculations volume 0, 5 m3. Liters it will be 0, 5 x 1000= 500 litres.

# Advice 3 : How to find the cross-sectional area of the cylinder

A cylinder is called a geometric solid formed by rotating a rectangle around one of the sides. Cut the cylinder by a plane in any direction. It would result in different geometric shapes. They need to build or even imagine in order to calculate the area of a cross section.

You will need

- - cylinder with the specified parameters;
- - location section.

Instruction

1

The cross section of the cylinder by a plane passing through its base, is always a rectangle. But depending on location these rectangles will be different. Find the area of the axial section perpendicular to the bases of the cylinder. One side of this rectangle is equal to the height of the cylinder, the second diameter of the rim base. Accordingly, the cross-sectional area in this case will be equal to the product of the sides of the rectangle. S=2R*h, where S is the cross-sectional area, R is the radius of the circular base, given the conditions of the problem, and h is the height of the cylinder, also specified the conditions of the problem.

2

If the cross-section perpendicular to the bases, but does not pass through the axis of rotation side of the rectangle equals the diameter of the circle. It has to be calculated. To this end, the conditions of the problem must be stated at what distance from the axis of rotation is the plane of the section. For computational convenience draw a circle of the cylinder base, slide the radius and mark on it the distance from the center of the circle is the cross section. From that point, swipe to the radius of the perpendiculars until they intersect with the circle. Connect the point of intersection with the center. You need to find the size of the chord. Find the size of half the chord by Pythagorean theorem. It will be equal to the square root of the difference of the squares of the radius of the circle and distance from center-line section. a2=R2-b2. The whole chord will be respectively equal to 2A. Calculate the cross-sectional area which is equal to the product of the sides of the rectangle, i.e. S=2a*h.

3

The cylinder can be cut and the plane not passing through the ground plane. If the cross section is perpendicular to the axis of rotation, it will be a circle. The area it is in this case equal to the area of grounds that is calculated by the formula S=πR2.

Useful advice

In order to better imagine the cross section, make a drawing and additional constructions to it.

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

In solving mathematical and technical problems sometimes it is necessary to know the volume

**of the cylinder**. A similar problem often arises in the everyday life, as many containers (drums, pails, cans, etc.) have a cylindrical shape. Of course, if you know the radius and height (length)**of the cylinder**, its volume is very easy to calculate. However, in practice these options are not always specified, and the cylinders are not only direct circular.You will need

- calculator

Instruction

1

To find the volume

**of a cylinder**, multiply its height by the number "PI" and the square of the radius. As a formula this rule as follows: = V * π * R2, where the volume**of the cylinder**, height**of cylinder**, R is the base radius**of the cylinder**, π is the number PI, approximately equal to 3.14.The volume**of the cylinder**to be measured corresponding to the radius and height of the cubic units of measurement. Ie if, for example, the radius and height**of cylinder**are given in meters, the volume will in cubic meters (m3).The above rule applies only for "normal", i.e. straight circular**cylinder**(**cylinder**, whose base is a circle, and the guide perpendicular to it).2

Example: height

**of cylinder**is 5 cm and the base radius is 2 cm In this case its volume will be equal: 5 * π * 22 ≈ 62,831 cm3.The number π has many calculators and denoted usually by the Greek letter "PI" (π). On the virtual keyboard the standard Windows calculator (in engineering), the number is denoted as pi.3

If instead the radius

**of the cylinder**is set the diameter, use the following formula: = V * π * (D/2)2 or = ¼ * H * π * D2, where D is the diameter of the base**of the cylinder**.4

Example: height and base diameter

**of the cylinder**is 10 cm In this case) to know the volume, calculate the value of the following expression: 10 * π * (10/2)2 ≈ 785,398 cm3.5

In practice, it is generally much easier to measure the perimeter (circumference) of the base

**of the cylinder**than its diameter or radius. To calculate the volume**of a cylinder**if you know the perimeter of his base, use the following formula:About = ¼ * B * N2 / p, where P is the perimeter of the base.When you use this formula to calculate the capacity of containers (dishes) please note that the actual capacity would be slightly less than calculated based on the volume of vessel walls).6

According to the definition, the base

- the volume

**of the cylinder**can be an arbitrary line in the plane, and its image is not necessarily perpendicular to the base. In the General case to know the volume**of the cylinder**by the following rules:- the volume**of a cylinder**equals the length of the forming to the cross-sectional area**of the cylinder**by the plane perpendicular to the generatrix;- the volume

**of a cylinder**equals the area of the base to the height (distance between bases).Note

The height of the cylinder - the concept is purely geometric. It means the distance between its bases and does not depend on the location of the cylinder in space.

# Advice 5 : How to find the area of the cylinder base

If the problem does not specify what cylinder it is (parabolic, elliptic, hyperbolic, etc.), it is assumed the easiest option. Such a spatial geometric shapes in the bases are circles and the lateral surface forms with them a right angle. Calculation of parameters in this case is not particularly difficult.

Instruction

1

If you know the radius (r) of the base cylinder, all the other dimensions are not important in the calculations. Calculate the product of the number PI rounded to the desired degree of accuracy, the squared radius is and the area of base of cylinder (S): S=π*r2. For example, if the diameter (which, as you know, twice the radius) of the cylinder is equal to 70cm, and the result of the computation is required to obtain accurate up to the second decimal place (hundredths of a centimeter), then the footprint will be 3,14*(70/2)2 = 3,14*352 = 3,14*1225 ≈ 3848,45см2.

2

If the radius and the diameter is unknown, but the height (h) and volume (V) of the cylinder, then these parameters will also be sufficient to find the area (S) of the Foundation figures, just divide the volume by the height: S=V/h. For example, if the volume is equal to 950см3 and height in 20cm cylinder will have a base area of 950/20=47,5см2.

3

If in addition the height (h) of the cylinder is known the area of its lateral surface (p), then to find the area of the base (S) take the lateral surface area in the square and divide the result by four times the product of the number PI squared height: S=p2/(4*π*h2). For example, if the lateral surface area equal 570см2, then at the height of the cylinder is 25cm and the desired accuracy of computations in one hundredth of a centimeter, it needs to have a footprint equal to 5702/(4*3,14*252) = 324900/(12,56*625) = 324900/7850 ≈ 41,39см2.

4

If besides the area of the lateral surface of the cylinder (p) are known and the area of the whole surface (P), then subtracting the second from the first, remember to divide the result in half, as the total area includes both bases of the cylinder: S=(P-P)/2. For example, if the total area of the spatial shape is 980см2, and the area of its lateral surface - 750см2, the area of each base is equal to (980-750)/2=115см2.

# Advice 6 : How to find the lateral surface area of a cylinder

Calculate the lateral surface area of a cylinder it is necessary in different situations. For example, you want to sew cushion cover-cushion and you need to determine the fabric consumption. Or are you going to paint round the barrel and have to calculate the amount of paint. Maybe your goal is to Wallpaper the walls in a round room? In all these cases, you will be faced with the task to determine the area of the lateral surface of the cylinder.

You will need

- Calculator, roulette or the tape

Instruction

1

The lateral surface of the cylinder in the expanded view is a rectangle.

The formula for calculating the area of the cylinder surface is simple:

Bok = LхH

where Bok — the desired lateral surface area of a cylinder.

The right part of the equality represented by the product of the two multipliers:

L is the measured length of the circumference of the cylinder, H is its height.

In turn, the circumference at the base of the cylinder is calculated by the formula:

L=PI x D

where PI — the number PI is a constant and is equal to 3.1416

D — diameter circle at the base of the cylinder.

A practical method of determining the area of the cylinder surface is chosen according to circumstances.

The formula for calculating the area of the cylinder surface is simple:

Bok = LхH

where Bok — the desired lateral surface area of a cylinder.

The right part of the equality represented by the product of the two multipliers:

L is the measured length of the circumference of the cylinder, H is its height.

In turn, the circumference at the base of the cylinder is calculated by the formula:

L=PI x D

where PI — the number PI is a constant and is equal to 3.1416

D — diameter circle at the base of the cylinder.

A practical method of determining the area of the cylinder surface is chosen according to circumstances.

2

Write down all your existing data on the cylinder, the lateral surface area which you need to determine.

If you know the height and diameter of the cylinder, then simply substitute in the formula for these parameters. Knowing the height and diameter of promotional stands, we can calculate the size of the poster. It is absolutely not necessary to see and measure cylindrical pedestal, on which is placed the poster.

If you know the height and diameter of the cylinder, then simply substitute in the formula for these parameters. Knowing the height and diameter of promotional stands, we can calculate the size of the poster. It is absolutely not necessary to see and measure cylindrical pedestal, on which is placed the poster.

3

Take a tape measure or measuring tape to determine the circumference of a circle at the base of the cylinder, if the cylinder is unknown.

In the absence of a flexible measuring tool you can do any rope, twine or braid. The circumference of the base of the cylinder define with a rope. The resulting segment of the rope, measure any measuring tools, such as tailor's ruler.

In the absence of a flexible measuring tool you can do any rope, twine or braid. The circumference of the base of the cylinder define with a rope. The resulting segment of the rope, measure any measuring tools, such as tailor's ruler.

4

Define the height of the cylinder.

When measuring the height of the cylinder, it is important to adhere strictly to the vertical to obtain an accurate result. To define the line vertical also useful for rope, the ends of which is tied to any load. For example, conventional nuts. One end of the rope attach to the base of the cylinder. Rope under the weight of the load is strictly vertical position. Along the line vertical and should be measure the height of the cylinder.

Multiply the two received measurements of the parameter. The result of the multiplication is the lateral surface area of a cylinder.

When measuring the height of the cylinder, it is important to adhere strictly to the vertical to obtain an accurate result. To define the line vertical also useful for rope, the ends of which is tied to any load. For example, conventional nuts. One end of the rope attach to the base of the cylinder. Rope under the weight of the load is strictly vertical position. Along the line vertical and should be measure the height of the cylinder.

Multiply the two received measurements of the parameter. The result of the multiplication is the lateral surface area of a cylinder.

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

The mass of any physical object helps to assess what force must be applied to move it in the absence of gravity and friction forces. But we often have to deal with the mass in another form, usually called "weight". It is defined as the force with which the physical body presses on the surface under the influence of gravity. To distinguish between these two forms of the mass are called "inertial" and "gravitational".

Instruction

1

Weigh the cylinder with weights desired degree of accuracy and get the value of its mass in terms of exposure to earth's gravity - the gravitational mass. This is the easiest, but not always available method applicable to physical objects not only of cylindrical shape.

2

If possible weigh not, then calculate the amount of space which is a cylindrical object and determine the density of the material of which it is composed. These two features are associated with a constant mass ratio, the formula which will calculate body mass. For determining the density of a substance will have to use relevant tables from the guides. In the paper version you can rent them in the library and in electronic form - find online or in the store on optical disks with thematic collections.

3

The volume of a cylinder you can determine the means at hand - for example, immerse it in the water-filled volumetric glassware, and assess the volume of displaced water. The value obtained is likely to be marked on the measuring instruments in liters and derived units. For payment in cubic meters and its derivatives use this ratio: one liter equal to one cubic decimeter.

4

If you define a volume (V) given in the previous step by the way is not possible, then determine the physical dimensions of the cylinder diameter (d) and height (h). Calculate the value of one quarter of the works of PI, taken with the necessary degree of precision on the squared diameter to find the area of the base of the cylinder. Multiply it by the height and get the volume of a cylindrical object is: V=¼*π*d*h.

5

Now you know the density (ρ), which comprises the cylinder, and its volume (V). To calculate the mass (m) of the object just multiply the two values: m=ρ*V.

# Advice 8 : How to measure the volume of a cylinder

Under the cylinder-to - understand geometric solid bases which are circles, and the angle between the side surface and the base is 90 degrees. To calculate the volume

**of a cylinder**, there are special formulas and methods. The use of a particular method of measurement is determined by the tools that you have.You will need

- measuring tools;
- calculator.

Instruction

1

Use for calculating volume

**of a cylinder**formula:V = H x S, where V is the volume**of the cylinder**; H-height; S – the area of one of the bases; x is a multiplication sign.This formula can be applied only in the case when the footprint is known from the conditions of the problem and requires no prior calculations. For example, if the height**of the cylinder**is 2 m and the area of one of its bases is equal to 3.5 m, then V = 2 x 3.5 = 7 cubic meters.2

If the footprint of unknown conditions previously perform a calculation. For this construct in the square is known or measured the radius of the circle lying at the base, and multiply it by the number "PI" equal approximately to 3.14. For example, if the radius is 1.2 m, the footprint is: S = 1.2 x 1.2 x 3,14 = of 4.52 sq. m. Now multiply the value by the height

**of the cylinder**to get volume.3

In the case of known diameter

**of the cylinder**and height calculate the volume of geometric solids according to the formula:V = 3,14 x H x D2 / 4, where V is the volume**of the cylinder**; 3,14 – the PI; H – height of**cylinder**; D – diameter; x – multiplication; / – division sign.So if the diameter of the circle lying at the base is 0.5 m, the height**of the cylinder**is 1.2 m, the volume will be: 3,14 x 1.2 x 0.5 x 0.5 / 4 = of 0.236 cubic meters.4

At a known length of the circumference of the base and height find the volume

**of the cylinder**as the product of the height**of the cylinder**to the quotient of the square of the circumference by the following formula:V = x L2 H / (3,14 x 4), where V is the volume**of the cylinder**; 3,14 – the PI; H – height**of the cylinder**; L is the length of the circle lying at the base**of the cylinder**.5

If you need to measure the real volume

**of the cylinder**, before carrying out calculations for one of the above formulas produce a measurement of the object by means of measuring instruments. To measure the linear parameters of the geometric body use a ruler, calipers, measuring cord or tape.6

Apply the principle of copying, if to measure parameters

**of the cylinder**in place is not possible. To do this, take a picture of the cylinder, including its base and height, by placing next to a ruler or object of known size, e.g. a matchbox. Then measure the size of photographs, transferring the data at the appropriate scale.