# Thread:

1. ## Please Help Final Tom!! Word Problem

Can someone please explain how to set up the equation for the following word problem,
-Express the surface area (S) of a rectangular box with a square base and of volume 100 ft.3 in terms of the length (x) of the square base.

2. Originally Posted by B1GG13
Can someone please explain how to set up the equation for the following word problem,
-Express the surface area (S) of a rectangular box with a square base and of volume 100 ft.3 in terms of the length (x) of the square base.
Hello,

the volume of the box is calculated by: $V=x^2 \cdot h~\iff~\boxed{h=\frac{V}{x^2}}$

The surface area consists of 2 squares and 4 congruent rectangles:

$s=2 \cdot x^2+4 \cdot x\cdot h~\implies~s(x)=2x^2+4\cdot x \cdot \frac{V}{x^2}~\iff~ s(x)=2x^2+4 \cdot \frac Vx$
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