Question

A rectangular solid with a square base has a volume of 4096 cubic inches - determine the dimensions that yield the minimum surface area

Answer 1

side of base, a = 10.1 inches, height, h = 40.1 inches

Explanation:

Volume of rectangular solid, V = 4096 cubic inches

Let the side of base is a and the height is h.

`V = a^2h\\\\4096 = a^2 h ..... (1)`

surface area of the solid

`S = 2a^2 + 4 ah \\\\S = 2a^2 + 4 * a * (4096)/(a^2) from (1)\\\S = 2a^2 + (4096)/(a)\\\\(dS)/(da)= 4 a - (4096)/(a^2)\\\\4 a - (4096)/(a^2) = 0 \\\\a^3 = 1024\\\\a =10.1 inches`

So, h = 40.2 inches