Two cubes have their volumes in the ratio 1 : 27.

Question:

Two cubes have their volumes in the ratio 1 : 27. The ratio of their surface areas is
(a) 1 : 3
(b) 1 : 8
(c) 1 : 9
(d) 1 : 18

Solution:

(c) 1 : 9

Suppose that the edges of the cubes are a and b.
We have:
a3b3=127ab3=127ab=13">

$\frac{a^{3}}{b^{3}}=\frac{1}{27}$

$\Rightarrow\left(\frac{a}{b}\right)^{3}=\frac{1}{27}$

$\Rightarrow \frac{a}{b}=\frac{1}{3}$

$\therefore$ Ratio of the surface areas $=\frac{6 a^{2}}{6 b^{2}}=\left(\frac{a}{b}\right)^{2}=\left(\frac{1}{3}\right)^{2}=\frac{1}{9}$

 

 

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