Solve
-An Open-Top Rectangular Box Has a Square Base and It

Multiple Choice

Solve.
-An open-top rectangular box has a square base and it will hold 256 cubic centimeters (cc) . Each side of the base has length $x \mathrm {~cm}$ . The box's surface area $S$ is given by
$$S ( x ) = \frac { 1024 } { x } + x ^ { 2 } .$$
Estimate the minimum surface area and the value of $x$ that will yield it.

A) $256 \mathrm {~cm} ^ { 2 }$ when $x = 6 \mathrm {~cm}$
B) $207 \mathrm {~cm} ^ { 2 }$ when $x = 6 \mathrm {~cm}$
C) $256 \mathrm {~cm} ^ { 2 }$ when $x = 8 \mathrm {~cm}$
D) $192 \mathrm {~cm} ^ { 2 }$ when $\mathrm { x } = 8 \mathrm {~cm}$