Answer: 2 units
Step-by-step explanation:
The lateral area of the cylinder is given by :-
[tex]L.A.=2\pi r h[/tex], where r is radius and h is the height of cylinder.
Given: The lateral area of the cylinder = 16π square units.
Let r be the radius of the triangle, then we have
Height of cylinder = 2r
The lateral area of the given cylinder will be :-
[tex]16\pi=2\pi r(2r)\\\\\Rightarrow2r^2=8\\\\\Rightarrow r^2=4\\\\\Rightarrow r=\pm2[/tex]
Hence, the length of the radius of the cylinder = 2 units.
