Question

will the surface area of a cylinder change if you double the height or double the radius explain your reasoning

Answer 1

let initial radius be r and height be h

Surface area of cylinder initially
 
SA = 2pi r h + 2 pi r^2 = 2pi (rh + r^2)

When radius is doubled 

r' = 2r
Thus
Surface area becomes

                   SA' = 2 pi r' h + 2 pi r'^2
                   SA' = 2 pi 2r h + 2 pi 4 r^2
                         = 2 pi (2 rh +  4r^2)
                         = 2 * 2 pi (rh+ 2r^2)
                        = 2 * [2 pirh + 2pir^2 + 2 pir^2]
                        = 2 * [ 2pi(rh+r^2) + 2 pi r^2]
                 SA' = 2*[SA + 2 pi r^2]