Question

A cylinder 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 please

Answer 1

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