# Formula And Examples to Calculate the Surface Area of a Cylinder

Mensuration is a very integral part of geometry, and it deals with the calculation of the area and volume of many geometrical shapes. Let's learn something new today!

ScienceStruck Staff

Last Updated: Jan 14, 2019

Formula for Surface Area of a Cylinder

You have to calculate the area for both the circles, and the cylindrical part in between. The cylindrical part in between is simply a rectangle that has been rolled up.

**lateral surface area**of a cylinder. The formula for the area of a circle is

*Πr*. The value

^{2}*Π*, or

*pi*, is a mathematical number calculated as 22÷7, or 3.14. Therefore, after using the formula and getting a number as its result, to find the total lateral surface area we simply multiply this number by 2.

*2Πr*. Next, we need to find the area of the rolled up rectangular part of the cylinder. This is known as the curved surface area.

^{2}*h*that we measured earlier, and the breadth is

*2Πr*. Hence, the formula for the curved surface area is

*2Πrh*.

Equation for Surface Area of a Cylinder

All we need to do is add up these two amounts, that is, the curved surface area and the lateral surface area.

Here's how to find the surface area of a right cylinder, which as a cylinder whose base is perpendicular to its sides.

Total Surface Area =

Total Surface Area =

Here's how to find the surface area of a right cylinder, which as a cylinder whose base is perpendicular to its sides.

Total Surface Area =

*2Πrh + 2Πr*^{2}Total Surface Area =

*2Πr(h + r)*Example

Assume that there is a cylinder with radius 5 cm and height 10 cm. Therefore,

Now, lateral surface area =

Curved surface area =

*r*= 5, and*h*= 10.Now, lateral surface area =

*2Πr*= 2 X 22/7 X 5 X 5 = 157.14^{2}Curved surface area =

*2Πrh*= 2 X 22/7 X 5 X 10 = 314.28^{2}

Alternately, you can apply the formula for total surface area directly as well.

Total surface area =

*2Πr(h + r)*= 2 X 22/7 X 5 (10 + 5) = 2 X 22/7 X 5 X 15 = 471.42 cm

^{2}