Question

Find a formula for the described function. An open rectangular box with volume 3 m3 has a square base. Express the surface area SA of the box as a function of the length of a side of the base, x.

Answer 1

`SA(x) = x^2 + (12)/(x)`

Explanation:

Given

`V = 3m^3` --- volume

`x \to base\ length`

`y \to height`

Required

The surface area as a function of base length

The volume (V) is calculated as:

`V = Base\ Area * Height`

`V = x*x*y`

`V = x^2*y`

Make y the subject

`y = (V)/(x^2)`

Substitute 3 for V

`y = (3)/(x^2)`

The surface area of the open box is:

`SA = x^2 + 2xy+2xy`

`SA = x^2 + 4xy`

Substitute:
`y = (3)/(x^2)`

`SA = x^2 + 4x*(3)/(x^2)`

`SA = x^2 + 4*(3)/(x)`

`SA = x^2 + (12)/(x)`

Hence, the function is:

`SA(x) = x^2 + (12)/(x)`