SOLUTION: I need to create a package(cylinder) with the smallest surface area and the largest volume. My package must be able to hold 450 grams so the volume should be 450 cm cubed since 1

Question 1074665: I need to create a package(cylinder) with the smallest surface area and the largest volume.
My package must be able to hold 450 grams so the volume should be 450 cm cubed since 1 gram=1 cm cubed.
I need help calculating the best answer so finding the lowest smallest surface area, but it should still have 450cm cubed as the volume.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
area is 2 pi r^2, to deal with the ends + 2 pi*r*h to deal with the wall.
V=450=pi*r^2*h
h=450/pi*r^2
A=2 pi*r^2+2*pi*r*(450/pi*r^2)
Take the derivative wrt r and set it equal to 0.
0=4pi*r-900/r^2
4pi*r=900/r^2
r^3=225/pi
r=4.15 cm
h=8.31 cm
V=pi*r^2*h=449.62 cm^3
Area is 108.21 cm^2+216.69 cm^2=324.90 cm^2.
------------------------------
check by looking at 143.13 as product of r^2*h
If r=5, h is 5.72
A is 157.08+ 179.70=336.78 cm^2
If r is 4, h is 8.95
A is 100.53+224.93=325.46 cm^2

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