Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
Two cubes have their volumes in the ratio 1 : 27. Find the ratio of their surface areas. (A.A.O. Exam, 2010)
Answer
SELF-PRACTICE — the source book printed no answer.
Nothing is invented here, so this question has no answer on record.
Explanation
Let their edges be $a$ and $b$. Then, $\frac{a^{3}}{b^{3}}=\frac{1}{27}$ or $\left(\frac{a}{b}\right)^{3}=\left(\frac{1}{3}\right)^{3}$ or $\frac{a}{b}=\frac{1}{3}$. $\therefore$ Ratio of their surface areas $=\frac{6a^{2}}{6b^{2}}=\frac{a^{2}}{b^{2}}=\left(\frac{a}{b}\right)^{2}=\frac{1}{9}$, i.e., 1 : 9.
Explanation as extracted from the printed page; notation may be imperfect.