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April 18, 2014

April 18, 2014

Posted by **NIKI** on Thursday, August 4, 2011 at 12:15pm.

(1) what value of x will produce the minimum outer surface area?

(2) What is the minimum surface area

- calculus -
**drwls**, Thursday, August 4, 2011 at 4:19pmVolume = x^2 h = 108 = constant

Surface Area = A (x) = x^2 + 4xh

= x^2 + 4x*108/x^2

= x^2 + 432/x

For minimum area,

dA/dx = 0

2x -432/x^2 = 0

x^3 = 216

x = 6 cm (and h = 108/36 = 3)

Minimum area = 36 + (432/6) = 108 cm^2

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