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 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 4 : 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.