Surface area is the sum of the field of all the faces of an object. In the case of Cylinder, it is a three-dimensional solid object with two circles as its base. It is one of the most basic of curvilinear geometric shapes. For example, you can consider a tin can with lids on the top and the bottom. To find the surface area of the cylinder first, we need to find the surface area of each base along with the surface area of the outer wall of the cylinder.

To find the surface area of the cylinder we will be using a formula which is A = 2πr^{2} + 2πrh. Where the “A” represents the area of the Cylinder and “h” represents the height of the cylinder. Let’s explore the formula step by step.

As we discussed earlier, we have to find the surface area of each face of the object and add them to calculate the Surface area of the cylinder. The cylinder has two circular bases. Let’s start by figuring each of the circle.

To calculate the area of a circle, we need to know the radius of the ring first. If you are doing any given task or problem, then the range of the circle or the value of the ‘r’ must be given as well. Sometimes the diameter of the circle is also given which is the distance from the one point on the outer surface of the circle to the right opposite point on the circle’s outer surface. The diameter is normally with’. If the diameter of the circle is given instead of radius, remember that the width is the twice of the radius. So you can get the radius by dividing diameter with 2. If you are performing any experiment practically, then you can calculate the measurement by using with a ruler.

After we got the radius of the circle, let’s start calculating the area of the circle. To find the area of a circle is the pi(~3.14) times the square of the radius of the circle. If we write it in a mathematical formula, it will be,

A = π x r^{2} – – – – – – – – – (Equation 1)

Where,

A= The area of the circle

r = The radius of the circle.

Let’s take an example for better understanding. Suppose we have a cylinder. The diameter of the circular base of the cylinder is 14cm, and the height of the cylinder is 10cm.

Now as we have the diameter of the circle (d = 14) instead of the radius, let’s calculate the radius first. The radius is the ½ of the diameter. So the radius of the circle = d/2

=14/2

=7cm

Hence, the radius of the circle is 7cm. Now we have the radius of the circle. Let’s calculate the area of the circle. If we put the given values in equation 1, the result will be,

A = π x r^{2}

= 3.14 X (7)^{2}

= 3.14 X 7 X 7

=153.86cm2

So the area of the circular base of the cylinder is 153.86cm^{2}. The two bases of a regular cylinder are identical. Which means the radius of the top circle will be as same as the bottom. Likewise, the area of the loop will also be the same. As we have already calculated the area of one circle, the other will also be the same.

After the bases come the cylindrical surface. If we cut the surface with a straight line, it’ll be a rectangle. As we have already known the height of the cylinder which is 10cm, we’ll only need the width of the rectangle. The width will be as same as the circumference of the circular base. As per the formula, the circumference will be, 2 X π X r = 2 X 3.14 X7 = 43.96cm

The area of the rectangle will be A = h X w = 10 X 43.96 = 439.6cm^{2}

The total surface area of the cylinder will be,

A = 2 x ( Area Of the Base) + Area of the Rectangle

= 2 x 153.86cm^{2}+ 439.6cm^{2}

= 307.72 + 439.6

= 747.32cm^{2}