Let
x------> the height of a cylinder
y------> the radius of a cylinder
we know that
x=5y
[the lateral area of the cylinder]=[perimeter of the base]*height
[perimeter of the base]=2*pi*r-------> 2*pi*y
[the lateral area of the cylinder]=[2*pi*y]*(5y)-----> 10*pi*y²
10*pi*y²=360*pi-----> y²=36--------> y=6 units
the answer is
the length of the radius of the cylinder is 6 units