Problem Solving

[Math Revolution GMAT math practice question]

If a cube A's volume is 216 times of a cube B's, the cube A's surface area is how many times of the cube B's?

A. 4
B. 8
C. 16
D. 25
E. 36

Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If a cube A's volume is 216 times of a cube B's, the cube A's surface area is how many times of the cube B's?

A. 4
B. 8
C. 16
D. 25
E. 36

\[?\,\, = \frac{{{S_A}}}{{{S_B}}} = \frac{{6 \cdot {{\left( {{\text{edg}}{{\text{e}}_A}} \right)}^2}}}{{6 \cdot {{\left( {{\text{edg}}{{\text{e}}_B}} \right)}^2}}} = \,\,{\left( {\frac{{{\text{edg}}{{\text{e}}_A}}}{{{\text{edg}}{{\text{e}}_B}}}} \right)^2}\]
\[{6^3}\,\,\, = \,\,\,216\,\,\, = \,\,\,\frac{{{V_A}}}{{{V_B}}}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,{\left( {\frac{{{\text{edg}}{{\text{e}}_A}}}{{{\text{edg}}{{\text{e}}_B}}}} \right)^3}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\frac{{{\text{edg}}{{\text{e}}_A}}}{{{\text{edg}}{{\text{e}}_B}}} = 6\,\,\,\,\,\,\,\,\,\,\,\left[ {\,\left( * \right)\,\,{\text{similar}}\,\,{\text{polyhedrons}}\,} \right]\]
\[? = {6^2} = 36\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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If the proportion between sides of cubes is a:b, the proportion between surface areas is a^2 : b^2 and the proportion between volumes is a^3 : b^3.
Since 216 = 63, the proportion is 216 : 1 = 6^3 : 1.
Thus the surface area of the cube A to that of the cube B is 6^2 : 1 = 36 : 1
Therefore, the answer is E.
Answer: E