The surface area of a cylinder is given by the sum of the lateral area and the area of both basis(the bottom base and the top). The base of a cylinder is a circle, therefore, the area of its base is
[tex]A_b=\pi r^2[/tex]where r represents the radius.
The lateral area of a cylinder is given by the formula
[tex]A_l=2\pi rh[/tex]where r represents the radius and h the height.
The total surface area is:
[tex]S=2A_b+A_l=2\pi r^2+2\pi rh=2\pi r(r+h)[/tex]Using the given values on the text, we have
[tex]S=2\cdot\pi\cdot4(4+5)=8\cdot\pi\cdot9=72\pi=226.08[/tex]The surface area of this cylinder is 226.08 in².
