Two cubes have volumes in the ratio 1 : 27. Then the ratio of the area of the face of one of the cubes to… · ABC26GN4878
Subject: General Aptitude · Chapter: Volume and Surface Area
Two cubes have volumes in the ratio 1 : 27. Then the ratio of the area of the face of one of the cubes to that of the other is
(a)1 : 3
(b)1 : 6
(c)1 : 9
(d)1 : 12
Answer
Answer (as printed): C
Explanation
Let their edges be $a$ and $b$. Then, $$\frac{a^{3}}{b^{3}}=\frac{1}{27} \Leftrightarrow\left(\frac{a}{b}\right)^{3}=\left(\frac{1}{3}\right)^{3} \Leftrightarrow \frac{a}{b}=\frac{1}{3} \Leftrightarrow \frac{a^{2}}{b^{2}}=\frac{1}{9} .$$
Explanation as extracted from the printed page; notation may be imperfect.