Minimum surface area box: All boxes with a square base and a volume of 50ft^3 have a surface area give by S(x) = 2x^2 + 200/x, where x is the length of the sides of the base. Find the absolute minimum of the surface area function. what are the dimensions of the box with minimum surface area.

I found the minimum surface area = (200/4)^1/3, but i failed to find the dimensions of the box.

Question

Minimum surface area box: All boxes with a square base and a volume of 50ft^3 have a surface area give by S(x) = 2x^2 + 200/x, where x is the length of the sides of the base. Find the absolute minimum of the surface area function. what are the dimensions of the box with minimum surface area.

I found the minimum surface area = (200/4)^1/3, but i failed to find the dimensions of the box.

anonymous · Answer

How did you find the minimum surface area?

anonymous · Answer

by taking the derivative of S(x), and equate it to zero

anonymous · Answer

And then you solved for?

anonymous · Answer

x...oh! so thats the dimension?

anonymous · Answer

so i plug in the x value into s(x) to find out the minimum surface area, and then plug in to V=50ft^3 to find out the height of the box?

anonymous · Answer

Well, that's a dimension certainly. Probably the length:width of the square base.

anonymous · Answer

yeah.

anonymous · Answer

thanks!