Acylinder has a height that is 5 times as large as its radius. the lateral area of the cylinder is 360π square units. what is the length of the radius of the cylinder? show work

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