Solve the Problem $x$ Height $y \mathrm {~cm}$ the Box's Surface Area Is Given By a Square

Multiple Choice

Solve the problem.
-An open-top rectangular box has a square base and it will hold 256 cubic centimeters (cc) . Each side has length $x$ height $y \mathrm {~cm}$ . The box's surface area 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) $256 \mathrm {~cm} ^ { 2 }$ when $x = 8 \mathrm {~cm}$
C) $192 \mathrm {~cm} ^ { 2 }$ when $x = 8 \mathrm {~cm}$
D) $108 \mathrm {~cm} ^ { 2 }$ when $x = 8 \mathrm {~cm}$