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09 Nov 2018, 01:25
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
86% (01:25) correct
14%
(02:09)
wrong
based on 57
sessions
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[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
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
09 Nov 2018, 01:41
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MathRevolution
Answer:
a^3 = 216 b^3, taking cube root of both the sides
a = 6 b, now squaring both the sides,
a^2 = 36 b^2, now we know that surface area of a cube is 6* square of side (6 a^2), multiplying each side by 6
6a^2 = 36* 6b^2,
this implies, surface area of cube a = 36 times surface area of cube b.
So, E is the correct answer.
09 Nov 2018, 02:26
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09 Nov 2018, 11:03
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MathRevolution
\(?\,\, = \frac{{{S_A}}}{{{S_B}}} = \frac{{6 \cdot {{\left( {{\text{edg}}{{\text{e}}_A}} \right)}^2}}}{{6 \cdot {{\left( {{\text{edg}}{{\text{e}}_B}} \right)}^2}}} = \,\,{\left( {\frac{{{\text{edg}}{{\text{e}}_A}}}{{{\text{edg}}{{\text{e}}_B}}}} \right)^2}\)
\({6^3}\,\,\, = \,\,\,216\,\,\, = \,\,\,\frac{{{V_A}}}{{{V_B}}}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,{\left( {\frac{{{\text{edg}}{{\text{e}}_A}}}{{{\text{edg}}{{\text{e}}_B}}}} \right)^3}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\frac{{{\text{edg}}{{\text{e}}_A}}}{{{\text{edg}}{{\text{e}}_B}}} = 6\,\,\,\,\,\,\,\,\,\,\,\left[ {\,\left( * \right)\,\,{\text{similar}}\,\,{\text{polyhedrons}}\,} \right]\)
\(? = {6^2} = 36\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
