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Posted by **Ben** on Monday, July 18, 2011 at 1:54pm.

Note: The side require 2pixh square inches of metal and each end requires pix^2 square inches.

- calculus -
**Reiny**, Monday, July 18, 2011 at 2:11pmVolume = πx^2h

h = 54/(πx^2)

Surface area = SA = 2πx^2 + 2πxh

SA = 2πx^2 + 2πx(54/(πx^2))

= 2πx^2 + 108/x

d(SA)/dx = 2πx - 108/x^2

= 0 for a min of SA

2πx = 108/x^2

x^3 = 108/(2π) = 54/π

x = (54/π)^(1/3) = appr. 2.58076

h = 54/(πª2.58076^2)) = appr. 2.58076

surprise! , the height should be equal to the radius.

- calculus -
**Ben**, Wednesday, July 20, 2011 at 4:42pmWhy did the 2ðx^2+108/x^2 become 2ðx-108/x^2

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