Question

A rectangular box is designed to have a square base and an open top. The volume is to be 2048in.3

What is the minimum surface area that such a box can have?

Answer 1

hi

Explanation:

Let x = the length of the sides of the base and h = the height:

Volume = (area of base)(height)

V = x2h

2048 = x2h

2048/x2 = h

Surface Area = area of base + 4(area of vertical side)

SA = x2 + 4xh

Eliminate the h by using 2048/x2 = h:

SA = x2 + 4x(2048/x2)

SA = x2 + 8192 x-1

Take the derivative of SA wrt x, set it to zero, solve for x. Plug that value of x into the surface area equation to find the minimum surface area.

Answer 2

x=y=z in 3 dimensions. So, you have x2y=4=x3⟹x=y=3√4.

Explanation: