The formula for the surface area of a cylinder is:
[tex]\sf A=2\pi rh+2\pi r^2[/tex]
Plug in what we know, use 3.14 to approximate for pi:
[tex]\sf 402\approx 2(3.14)(4)h+2(3.14)(4)^2[/tex]
Simplify:
[tex]\sf 402\approx 25.12h+100.48[/tex]
Subtract 100.48 to both sides:
[tex]\sf 301.52\approx 25.12h[/tex]
Divide 25.12 to both sides:
[tex]\sf h\approx\boxed{\sf 12.0~cm}[/tex]
So the height is approximately 12 centimeters.
