If an open box has a square base and a volume of 106 in.3 and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction. (Round your answers to two decimal places.)

Question

height in
length in
width in

Answer 1

V = L*W*H = 106in^3,

Since the base is square,
W = H.
L*W*W = 106,
L*W^2 = 106,
To minimize the material,
let L = W:
W*W*W = 106,
W^3 = 106,
W = crt(106) = 4.73in.
L = 4.73in.
H = 4.73in.