Question 969172
i couldn't find any other way to do it without using calculus, so i solved it by graphing.


i got r = 4.025946 and h = 8.051894821.


with those values, surface area = 2 * pi * r * h + 2 * p * r^2 = 305.51822


the graph of the equation for surface area looks like this.


<img src = "http://theo.x10hosting.com/2015/050801.jpg" alt="$$$" </>


the formula for surface area used was:


y = 2 * pi * x * (410/(pi * x^2)) + 2 * pi * x^2


y represents the surface area.
x represents the radius.
h is equal to (410 / (pi * r^2))


this was derived by solving for h in the volume formuls of v = pi * r^2 * h.


when v is equal to 410, this formula became 410 = pi * r^2 * h.


this led to h = (410 / (pi * r^2)).


the formula could have been simplified further but i left it the way it was so you could see the value of h in terms of r stand out more clearly.


the area on the graph of interest is when x and y are both greater than 0.