If a cube A’s volume is 216 times of a cube B’s, the cube A’s surface

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

bashdeep · Answer

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.

dollytaneja51 · Answer

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fskilnik · Answer

?\,\, = \frac{{{S_A}}}{{{S_B}}} = \frac{{6 \cdot {{\left( {{	ext{edg}}{{	ext{e}}_A}} ight)}^2}}}{{6 \cdot {{\left( {{	ext{edg}}{{	ext{e}}_B}} ight)}^2}}} = \,\,{\left( {\frac{{{	ext{edg}}{{	ext{e}}_A}}}{{{	ext{edg}}{{	ext{e}}_B}}}} ight)^2}

{6^3}\,\,\, = \,\,\,216\,\,\, = \,\,\,\frac{{{V_A}}}{{{V_B}}}\,\,\,\mathop = \limits^{\left( * ight)} \,\,\,{\left( {\frac{{{	ext{edg}}{{	ext{e}}_A}}}{{{	ext{edg}}{{	ext{e}}_B}}}} ight)^3}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\frac{{{	ext{edg}}{{	ext{e}}_A}}}{{{	ext{edg}}{{	ext{e}}_B}}} = 6\,\,\,\,\,\,\,\,\,\,\,\left

? = {6^2} = 36

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

Regards, 
Fabio.

MathRevolution · Answer

=>
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

ScottTargetTestPrep · Answer

We can let a = the length of an edge of cube A and b = the length of an edge of cube B. We can create the equation:

a^3 = 216b^3

a = 6b

So if b is 1, a is 6.

The surface area of B is 6 x 1^2 = 6.

The surface area of A is 6 x 6^2 = 216.

So the surface area of A is 216/6 = 36 times the surface area of B.

Answer: E

If a cube A’s volume is 216 times of a cube B’s, the cube A’s surface

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If a cube A’s volume is 216 times of a cube B’s, the cube A’s surface

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