In order to calculate the area surface of a circular right cylinder you have to calculate the area of the bottom and top circles, and the area of the rectangle/square formed by imaginary unfolding the side of the cylinder as is shown in the image below.

The bottom and the top circles are identical. The area of a circle is πr^{2}. Since we have 2 circles, we have to multiply the result by 2.

To find out the area of the rectangle formed by unfolding the side of the cylinder we have to know its height and its base. The base equals the perimeter (also widely known as circumference) of the circle so the area will be perimeter of the bottom circle multiplied by the height of the cylinder. We also know the circumference of a circle is π2r.

Area of the bottom circle = πr^{2}

Area of the top circle = πr^{2}

Area of the side of the cylinder = π2rh

Area of the cylinder = 2πr^{2} + π2rh

Example:

If *r = 5 units* and *h = 9 units* then the A (Area Cylinder) = ?

A = 2 × 3.14 × 25 + 3.14 × 2 × 5 × 9 =

= 157 + 282.6 =

= 439.6 units^{2}