A box has rectangular sides, top and bottom. The volume of the box is 3 cubic meters. The height of the box is half the width of the base. Express the total surface area of the box in terms of the height of the box.

Answer 1

If the height is h, then the base has dimensions 2h and y, so

2h^2y = 3
so y = 3/(2h^2)

and the area is two pairs of vertical faces:

2(2h*h + y*h) = 2(2h^2+3/(2h^2)*h)
= 4h^2 + 3/h