Cylinder Area | Tutorela

Calculation of the area of a cylinder

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

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:

$A=2XR(R+H)$

Lateral surface area

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:

$S= 2XRH$