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.