Choose the one alternative that best completes the statement or answers the question.
-A closed box with a square base has to have a volume of 16,000 cubic inches. Find a function for the surface area of the box.
A) $S ( x ) = x ^ { 2 } + \frac { 64,000 } { x }$
B) $S ( x ) = 2 x ^ { 2 } + \frac { 64,000 } { x }$
C) $S ( x ) = 2 x ^ { 2 } + \frac { 16,000 } { x }$
D) $S ( x ) = 2 x ^ { 2 } + \frac { 96,000 } { x }$

Question

Quizplus · Accepted Answer

The surface area $S$ of a box with a square base and volume $V = 16,000$ cubic inches can be found using the formula for the volume $V = x^2h$, where $x$ is the side length of the square base and $h$ is the height. Solving for $h$, we get $h = \frac{V}{x^2} = \frac{16,000}{x^2}$. The surface area of the box is the sum of the areas of the four sides and the two bases: $S = 2xh + 2xh + 2x^2 = 4xh + 2x^2$. Substituting $h$ gives $S = 4x(\frac{16,000}{x^2}) + 2x^2 = \frac{64,000}{x} + 2x^2$, which matches choice B.

Choose the One Alternative That Best Completes the Statement or Answers