ABC26GN4877 · Volume and Surface Area
Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
The volumes of two cubes are in the ratio 8 : 27. The ratio of their surface areas is
(a)2 : 3
(b)4 : 9
(c)12 : 9
(d)None of these
Answer
Explanation
Let their edges be $a$ and $b$. Then, $$\begin{aligned} \frac{a^{3}}{b^{3}}=\frac{8}{27} \Leftrightarrow\left(\frac{a}{b}\right)^{3}=\left(\frac{2}{3}\right)^{3} \Leftrightarrow \frac{a}{b}=\frac{2}{3} & \Leftrightarrow \frac{a^{2}}{b^{2}}=\frac{4}{9} \\ \Leftrightarrow & \frac{6 a^{2}}{6 b^{2}}=\frac{4}{9} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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