Answer:
looks like school work
Step-by-step explanation:
DO IT ON YOUR OWN
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Answer:
30
Step-by-step explanation:
Let h = height of the box,
x = side length of the base.
Volume of the box is

.
So

Surface area of a box is S = 2(Width • Length + Length • Height + Height • Width).
So surface area of the box is


The surface are is supposed to be the minimum. So we'll need to find the first derivative of the surface area function and set it to zero.

![4x = \frac{460}{ x^{2} } \\ 4x^{3} = 460 \\ x^{3} = 115 \\ x = \sqrt[3]{115} = 4.86](https://tex.z-dn.net/?f=%204x%20%3D%20%5Cfrac%7B460%7D%7B%20x%5E%7B2%7D%20%7D%20%20%5C%5C%20%204x%5E%7B3%7D%20%3D%20460%20%20%5C%5C%20x%5E%7B3%7D%20%3D%20115%20%20%5C%5C%20x%20%3D%20%20%5Csqrt%5B3%5D%7B115%7D%20%3D%204.86%20)
Then

So the box is 4.86 in. wide and 4.87 in. high.