Question

An open rectangular box with volume 9 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

Answer:

The surface area of the box as a function of the length of a side of the base is $S=x^2+\frac{36}{x}$.

Step-by-step explanation:

Let $x$ be the length side of the square base and $y$ be the height of the box.

According with the diagram the volume of a rectangular box with a square base is given by

$V=x^2\cdot y$

and we know that its value is 9 $m^3$.

The surface area is given by

S = (Area of Base) + 4(Area of a Vertical Side)

$S=x^2+4\cdot x\cdot y$

From the volume formula we can solve for $y$

$9=x^2\cdot y\\y=\frac{9}{x^2}$

and substitute into the surface area formula

$S=x^2+4\cdot x\cdot \frac{9}{x^2} \\S=x^2+\frac{36}{x}$