geometry is actually so hard its not even funny

The total surface area of right circular cylinder is \(\pi d(r+h)\)
In the diagram: \(d=(4x+2),~r=(2x+1),~\&~h=2x\).
 
In a little more detail, the surface of this cylinder consists of two disk with diameter equal to the diameter of the cylinder and the cylindrical "side".

The area of a disk with diameter 4x+ 2 (so radius 2x+ 1) is \(\displaystyle \pi(2x+ 1)^2\) so the area of the top and bottom is \(\displaystyle 2\pi(2x+ 1)^2\).

To find the area of the side, imagine cutting it vertically and opening it out to form a rectangle. The width of that rectangle is the height of the cylinder, 2x. The length is what previously was the circumference of the cylinder, \(\displaystyle \pi\) time the diameter, \(\displaystyle \pi (4x+ 2)\). So the total surface area is \(\displaystyle 2\pi(2x+ 1)^2+ \pi(4x+ 2)\).
 
This really is not that hard.
You have the top whose surface area is pi*r^2. After all, it is just a circle.
The bottom being a circle also has a surface area of pi*r^2
If you unroll the side of the cylinder it would be a rectangle. The length of the rectangle is equal to the circumference of the circle which is 2pi*r and the height is h. Therefore the surface area of the side is 2pi*r*h.
Adding the three pieces together gives you 2pi*r^2 + 2pi*r*h = 2pi*r(r+h)
 
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