Mathematics: 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.

Find a formula for the described function. An open

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18.07.2021

$SA(x) = x^2 + \frac{12}{x}$

Step-by-step 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

$y = \frac{V}{x^2}$

Substitute 3 for V

$y = \frac{3}{x^2}$

The surface area of the open box is:

SA = x^2 + 2xy+2xy

SA = x^2 + 4xy

Substitute: $y = \frac{3}{x^2}$

$SA = x^2 + 4x*\frac{3}{x^2}$

$SA = x^2 + 4*\frac{3}{x}$

$SA = x^2 + \frac{12}{x}$

Hence, the function is:

$SA(x) = x^2 + \frac{12}{x}$

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