Cylinder Area

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 AA). The area of the base is πR2πR^2 And to obtain the area of the two bases we multiply by 22, that is, 2×πR22\times πR^2.

To calculate the lateral area, we return to the sliced form. The width of therectangle is HH While the length of the rectangle (we denote it by LL) is equal to the circumference of the circle. The circumference of the circle is calculated using the formula. R×L=2XR\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×H=2X 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. R2XR 2X And we obtain the following formula:


Lateral surface area

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

The formula is:


Examples and Practice of the Cylinder

Exercise No. 1

Given the cylinder shown in the figure.

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


What is the total surface area of the cylinder: ?


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

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

Lateral surface area  

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

Total surface area of the cylinder: 

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


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

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


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

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