Answer:
1 ft
Step-by-step explanation:
If r is the radius of the circular top and bottom and h is the height of the cylinder, then the surface area of the cylinder is
[tex]A=2\pi r^2+2\pi rh.[/tex]
In your case, h=2 ft and [tex]A=6\pi\ft^2.[/tex]
Hence,
[tex]6\pi =2\pi r^2+2\pi r\cdot 2,\\ \\6\pi=2\pi(r^2+2r),\\ \\r^2+2r=3,\\ \\r^2+2r-3=0,\\ \\D=2^2-4\cdot (-3)=4+12=16,\\ \\r_{1,2}=\dfrac{-2\pm 4}{2}=-3,\ 1.[/tex]
The radius cannot be negative, then r=1 ft.
