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Ratio of surface areas of two cubes is $25 : 36$ Find the ratio of their volumes.

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25 : 16

12 : 21

15 : 26

125 : 216

answer is D.

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Detailed Solution

Given,
The ratio of surface areas of two cubes =

25 : 36

Suppose that,
The side of 1st cube = a
The side of 2nd cube = b
We know that
Surface area of cube

= 6 x^{2}

\frac{surface  area 1 st cube}{surface area 2 nd  cube} = \frac{25}{36}

Thus,

\frac{6 a^{2}}{6 b^{2}} = \frac{25}{36}

\Rightarrow \frac{a}{b} = \sqrt{\frac{25}{36}}

\frac{a}{b} = \frac{5}{6}

a

b = 5 : 6

Now, calculate the volume of the cube =

x^{3}

\frac{volume of 1 st cube}{volume of 2 nd cube} = \frac{a^{3}}{b^{3}}

Thus,

\frac{a^{3}}{b^{3}} = \frac{5^{3}}{6^{3}}

\frac{a^{3}}{b^{3}} = \frac{125}{216}

a^{3} : b^{3} = 125 : 216

Hence the ratio of the volume of two cubes

= 125 : 216

.
Option 4 is correct.

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