Find the dimensions of an open rectangular box with a square base that holds 2000 cubic cm and is constructed with the least building material possible.

Step-by-step explanation:

Let us assume that the dimension of the square base = S x S

Let us assume the height of the rectangular base = H

So, the total area of the open rectangular box  

= Area of the base +  4 x ( Area of the adjacent faces)

=  S x S  +  4 ( S x H)   = S² +  4 SH   ..... (1)

Also, Area of the box  = S x S x H  =  S²H

⇒ S²H = 2000

Substituting the value of H in (1), we get:

Now, to minimize the area put :

Putting the value of S  = 15.874 cm in the value of H , we get:

Hence, the dimensions of the given rectangular box are:

L  =   15.874 cm

B  = 15.874 cm

H = 7.8937 cm