An open-top box with a square base is to have a volume of 4 cubic feet. Find the dimensions of the box (in ft) that can be made with the smallest amount of material.

The dimension of box=

Step-by-step explanation:

We are given that

Volume of box=4 cubic feet

Let x be the side of square base and h be the height of box

Volume of box=

Now, surface area of box,A=

Substitute x=2

Hence, the area of box is minimum at x=2

Therefore, side of square base,x=2 ft

Height of box,h=

Hence, the dimension of box=

sss (side, side, side)

sas (side, angle, side)

asa (angle, side, angle)

aas (angle, angle, side)

hl (hypotenuse, leg)