You will need

- line;
- calculator;
- the notion of circle area and circumference.

Instruction

1

Determine

**the area of the**bases**of the cylinder**. To do this, measure with a ruler the diameter of the base, then divide it by 2. This will be the base radius**of the cylinder**. Calculate**the area of**a single base. To do this, lift the value of its radius squared and multiply by a constant π, Kr= π∙R2 where R is the radius**of the cylinder**, and π≈3,14.2

Find the total

**area**of the two bases, based on the definition**of the cylinder**, which suggests that its base are equal. The area of one circle of the base, multiply by 2, On=2∙Kr=2∙π∙R2.3

Calculate

**the area of**the lateral surface of the**cylinder**. To do this, find the circumference, which restricts one of the bases**of the cylinder**. If the radius is already known, we calculate it by multiplying the number of 2 π and the base radius R, l= 2∙π∙R, where l is the circumference of the base.4

Measure the length of the generatrix

**of the cylinder**, which is equal to the length of a segment connecting corresponding points of the base or their centers. In a typical straight cylinder forming L is numerically equal to its height H. Calculate**the area of**the lateral surface**of a cylinder**by multiplying the length of its base for forming BOC= 2∙π∙R∙L.5

Calculate

**the area**of the surface**of the cylinder**, by adding up**the area**of bases and lateral surface. S=On+ Bok. Substituting the formulae the values of the surfaces, obtain S=2∙π∙R2+2∙π∙R∙L, bring the total multipliers S=2∙π∙R∙(R+L). This will calculate the surface**of the cylinder**by means of a single formula.6

For example, the diameter of the base of a direct

**cylinder**is 8 cm and its height is 10 cm, Determine**the area of**its lateral surface. Calculate the radius**of the cylinder**. It is equal to R=8/2=4 cm Forming a direct**cylinder**is equal to its height, i.e. L=10 cm For calculations using a single formula, it's more convenient. Then S=2∙π∙R∙(R+L), substitute the corresponding numerical values S=2∙3,14∙4∙(4+10)=351,68 cm2.# Advice 2: How to calculate the height of a cylinder

Have the cylinder has a height that is perpendicular to the two bases. The way to determine its length depend on the input data set. These may be in particular the diameter, area, diagonal section.

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)