A cylinder must be distinguished between **total surface area** and **lateral surface area**.

A cylinder must be distinguished between **total surface area** and **lateral surface area**.

**Total surface area** is the sum of the areas of the two bases and the lateral area (marked as $A$). The area of the base is $πR^2$ And to obtain the area of the two bases we multiply by $2$, that is, $2\times πR^2$.

To calculate the lateral area, we return to the sliced form. The width of therectangle is $H$ While the length of the rectangle (we denote it by $L$) is equal to the circumference of the circle. The circumference of the circle is calculated using the formula. $R\times L=2X$.

From this we get that the lateral area is the area of the sliced rectangle, and we must multiply the length of the rectangle by the width of the rectangle.

The area of the resulting rectangle is $R\times H=2X$.

To obtain the total surface area, we will add the area of the two bases and the lateral area. We will eliminate a common factor outside of the parentheses. $R 2X$ And we obtain the following formula:

$A=2XR(R+H)$

**The lateral surface area** is just the lateral surface, without the bases (marked as $S$). That is, we refer to the area of the sliced rectangle, which we have already calculated for the total surface area.

**The formula is:**

$S= 2XRH$

Given the cylinder shown in the figure.

Depending on the data, one must find the lateral surface area and the total surface area.

**Task:**

What is the total surface area of the cylinder: ?

**Solution: **

From the figure, it can be observed that the radius of the bases is $R=5$ cm, and the height of the cylinder is $H=10$ cm.

Now it only remains to apply the formulas we have learned.

Lateral surface area

$S= 2πRH = 2\times 3.14\times 5\times 10= 314$

**Total surface area of the cylinder: **

$A= 2πR(R+H) = 2\times 3.14\times 5( 5+10)= 471$

**Answer:**

The lateral surface is $314$ cm², the total surface is $471$ cm².

**If you are interested in this article, you might be interested in the following articles:**

Cylinder

Volume of a cylinder

Right triangular prism

The bases of the right triangular prism

The lateral faces of the prism

Lateral edges of a prism

Height of the prism

Surface area of triangular prisms

**In the** **Tutorela**** blog, you will find a wide variety of mathematics articles**

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