let

r = the radius of the cylinder, r>o

h = the height of the cylinder, h>0

the surface area of a cylinder is 198pi square yards

2*r^2*pi + 2r*pi*h = 198pi divide both sides by pi

2*r^2 + 2rh = 198

the height of the cylinder is ten times the radius

h = 10r

plug h = 10r into 2*r^2 + 2rh = 198

2*r^2 + 2r*10r = 198

by solving we find

r = 3 yd

click here to see the step by step solution of the equation

the radius of the cylinder is 3 yards.