If the volumes of two cubes are in the ratio 27 : 1, the ratio of their edges is · ABC26GN4876
Subject: General Aptitude · Chapter: Volume and Surface Area
If the volumes of two cubes are in the ratio 27 : 1, the ratio of their edges is
(a)1 : 3
(b)1 : 27
(c)3 : 1
(d)27 : 1
Answer
Answer (as printed): C
Explanation
Let their edges be $a$ and $b$. Then, $\frac{a^{3}}{b^{3}}=\frac{27}{1} \Leftrightarrow\left(\frac{a}{b}\right)^{3}=\left(\frac{3}{1}\right)^{3}$ $$\Leftrightarrow \frac{a}{b}=\frac{3}{1} \Leftrightarrow a: b=3: 1 \text {. }$$
Explanation as extracted from the printed page; notation may be imperfect.