Question 1033470
Hi there,
π x r^2 x h = 500cc
h = 500/πr^2
Surface Area:
π x diameter x height + 2 x π x r^2
Using:
h = 500/πr^2
&#960 x 2r (diameter)x 500/πr^2
Area = 1000/r + 2πr^2
Area = 1000r^-1 + 2πr^2
Area (differentiated) 
= -1000r^-2 + 4πr
-1000r^-2 + 4πr = 0
-1000/r^2 + 4πr = 0
-1000/r^2 = -4πr (Multiply both sides by -1)
 1000/r^2 = 4πr 
1000 = 4&#960r^3
Divide both sides by 4
250 = πr^3
r^3 = 250/π
r = 3√250/π
r = 4.3
..........
Using Nature Table:       -   4.3   +
 .................. .......... .........                      \   -    /
Minimum.
...............
To establish height and radius
πr^2h = 500
π(4.3)^2h = 500
height = 500/(π(4.3)^2
Height = 8.6 centimeters
Radius = 4.3 centimeters
so, Diameter = 8.6 diameters.
Hope this helps :-)