Question 967660
you are given that S = 2 * pi * r * h.


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.


<a href = "https://www.google.com/?gws_rd=ssl#q=surface+areea+of+a+cylinder" target = "_blank">https://www.google.com?gws_rd=ssl#q=surface+areea+of+a+cylinder</a>


here's what the output looks like after you enter 1.64...... for the radius and 10 for the height.


<img src = "http://theo.x10hosting.com/2015/050201.jpg" alt="$$$" </>


the quadratic formula is:



<pre>
               (-b plus or minus sqrt(b^2 - 4ac)
         x =   -----------------------------------
                                (2a)
</pre>


your quadratic equation is :


2 * pi * r^2 + 20 * pi * r - 120 = 0


a = 2 * pi
b = 20 * pi
c = -120