Determine the Dimensions of a Rectangular Solid (With a Square $\frac { 23 \sqrt { 6 } } { 3 } \times \frac { 23 \sqrt { 6 } } { 3 } \times \frac { 23 \sqrt { 6 } } { 6 }$

Multiple Choice

Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 529 square meters.

A) Dimensions: $\frac { 23 \sqrt { 6 } } { 3 } \times \frac { 23 \sqrt { 6 } } { 3 } \times \frac { 23 \sqrt { 6 } } { 6 }$
B) Dimensions: $\frac { 23 \sqrt { 6 } } { 6 } \times \frac { 23 \sqrt { 6 } } { 6 } \times \frac { 23 \sqrt { 6 } } { 3 }$
C) Dimensions: $\frac { 23 \sqrt { 6 } } { 3 } \times \frac { 23 \sqrt { 6 } } { 3 } \times \frac { 23 \sqrt { 6 } } { 3 }$
D) Dimensions: $\frac { 23 \sqrt { 6 } } { 6 } \times \frac { 23 \sqrt { 6 } } { 6 } \times \frac { 23 \sqrt { 6 } } { 6 }$
E) Dimensions: $\frac { 529 \sqrt { 6 } } { 6 } \times \frac { 529 \sqrt { 6 } } { 6 } \times \frac { 23 \sqrt { 6 } } { 6 }$