Formula for volume and surface area of a cylinder and explain why

V = πr² * h (where r is the radius and h the height)
Total SA = Lateral Area + 2Base Area

LA = 2πr * h
BA = πr²

Why?

The cylinder is made by rotating a rectangle for 360°. Two sides make the top and bottom faces, that are circles. The radius is the dimension of the widht/lenght that generated the circles. The other sides form the lateral face (the cylinder has only one lateral face).

Of course to find the lateral area you multiply the radius for 2, to find the diameter of the circle and multiply for π since the rectangle rotates.

For the circles, the base area is just the formula to find the area of a circumference.

You sum the two areas (two times the base area, since it has a circle on the top and one on the bottom) to find the total area.

For the volume, that is the profondity, the capacity of the cylinder, you find the base area (so you know all the capacity) and multiply for the height.