Explanation:
the volume is
base area × height
the base area is a circle, and the area of a circle is
pi×r²
in our case the volume is
pi×5²×22 = pi×25×22 = 550pi = 1,727.875959... cm³
the surface area is the sum of
2 circles (top and bottom) = 2× pi×5²
the lateral area
the lateral area (the "mantle wall" of the cylinder) you can imagine to be cut open and then placed flat on a table.
in this case you can see it is just a rectangle, with the cylinder height being the width, and the circle circumference being the length.
the circle circumference is
2×pi×r = 2×pi×5 = 10pi = 31.41592654... cm
so, the lateral area is
22 × 31.41592654... = 691.1503838... cm²
the surface area is then
691.1503838... + 2×pi×25 = 691.1503838... + 50pi =
= 848.2300165... cm²