Explanation:

The surface area of cone = π x r x r + π x r x l where l is the slant height and r is the radius of the base.
Therefore we have, π x r x (r + l) = 217, 
which is same as π x 3.5 x (3.5 + l) = 217.
Therefore, the slant height = 16 5 / 22 cm.