AP:what is the radius of a cylindrical soda can with volume

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AP:what is the radius of a cylindrical soda can with volume of 512 cubic inches that will use
what is the radius of a cylindrical soda can with volume of 512 cubic inches that will use the minimum material?

V = pi*r^2*h = 512
A = 2*pi*r*h + 2*pi*r^2
h = 512/(pi*r^2)
A = 2*pi*r*512/(pi*r^2) + 2*pi*r^2 = 1024/r + 2*pi*r^2
dA/dr = -1024/r^2 + 4*pi*r = 0
r = 4.3554
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