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Q. An open-top box with a square base is to have a volume of 62.5 square inches. What dimensions will yield the box of minimum surface area?

I am getting 5" by 2.5" but not sure.

2 answers

(s^2)h=V
h=V/(s^2)=62.5/s^2
Surface area = 4hs +s^2
=4(62.5/s^2)s +s^2
=250/s + s^2

Derivative of surface area = -250/s^2 + 2s
0=-250/s^2 + 2s
250/s^2=2s
250=2s^3
125=s^3
s=5
h= 62.5/s^2=62.5/25 = 2.5
You are correct!
Thanks