Assuming the surface area includes the top and bottom circles, the total surface area is 2(pi)r^2+2(pi)rh where r=radius and h=height. That expression can be written 2(pi)r(r+h). The total surface area is given as 1859 sq cm and the height is 11.1cm. If the surface area does not include the end circles then 2(pi)r*11.1=1859 and r=26.655cm, so the diameter is 53.31cm. If the end circles are included, then we have to solve 2(pi)r(r+11.1)-1859=0. That is r^2+11.1r-(1859/(2(pi))=0. r^2+11.1r-295.869=0. Use the quadratic formula to get (-11.1+/-sqrt(123.21+1183.476))/2. The positive root is the only sensible one=12.524cm. So diameter=25.05cm.