Answer:
[tex][/tex] Let the radius of the cylinder be r and the height be h.
Given that the surface area of the cylinder is 588π, we can write the formula for the surface area of a cylinder as:
2πrh + 2πr² = 588π
Since the radius is twice the height, we can write:
r = 2h
Substitute r = 2h into the surface area formula:
2π(2h)h + 2π(2h)² = 588π
4πh² + 8πh² = 588π
12πh² = 588π
h² = 49
h = [tex] \sqrt49[/tex]
h = 7
Now, substitute h = 7 back into r = 2h:
r = 2(7)
r = 14
Therefore, the radius of the cylinder is 14 units and the height is 7 units.