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Re: If the ratio of the surface areas of the two similar cubes in the figu [#permalink]
Expert Reply
We can use estimation because the answer choices are pretty far apart

Surface area of a cube it is just the side by side of a single face of a cube and then times 6

6a^2

The volume of the cube is V = L×B×H.

We do know that the surface area is in the ratio of 9:25

a and b are the small and big cubes

\(\frac{6a^2}{6b^2}=\frac{9}{25}\)

or \(\frac{a}{b}=\frac{3}{5}\)

We do know that the volume of the small one is 54. Take the cube root of it and we do have the side a^3=54=3.7

Substitute

\(\frac{3.7}{b}=\frac{3}{5}\)

\(b=6.1\)

Now we do have b and we can calculate its volume

\(b=6.1^3 \approx 227\)

Only B is near enough
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