that would be the lateral area only.
it does not include the area of the bases.
if the formula you show is the formula you are given, then:
S = 2 * pi * r * h becomes 120 = 2 * pi * r * 10.
simplify to get 120 = 20 * pi * r
divide both sides of the equation by (20 * pi) and you get:
120 / (20 * pi) = r
solve for r to get r = 6 / pi.
you can leave it that way or you can simplify further to get r = 1.909859317.
you can confirm by replacing r with 1.909859317 and you will get 120 = 120.
now, the surface area of of a right cylinder is equal to the lateral area plus the base area.
that formula is S = 2 * pi * r * h + 2 * pi * r^2.
that's going to make a difference in what the radius turns out to be.
if that's the formula you need, then:
S = 2 * pi * r * h + 2 * pi * r^2 becomes:
120 = 2 * pi * r * 10 + 2 * pi * r^2
simplify to get:
120 = 20 * pi * r + 2 * pi * r^2
subtract 120 from both sides of the equation and re-arrange the terms and commute the equation to get:
2 * pi * r^2 + 20 * pi * r - 120 = 0
that's a quadratic equation in standard form that can be solved using the quadratic formula.
you will get:
Roots: -11.64067716, 1.640677162
negative value is no good.
r has to be 1.640677162 if we did everything correctly.
confirm by replacing that value of r in the original equation with 1.640677162 and you will see that the surface area is equal to 120.
here's an online calculator to give you the surface area of cylinder.
https://www.google.com?gws_rd=ssl#q=surface+areea+of+a+cylinder
here's what the output looks like after you enter 1.64...... for the radius and 10 for the height.
the quadratic formula is:
(-b plus or minus sqrt(b^2 - 4ac)
x = -----------------------------------
(2a)
your quadratic equation is :
2 * pi * r^2 + 20 * pi * r - 120 = 0
a = 2 * pi
b = 20 * pi
c = -120