Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2007 · Marks: · Difficulty:
How many small cubes, each of 96 cm surface area, can be formed from the material obtained by melting a larger cube of 384 cm surface area?
(a)5
(b)8
(c)800
(d)8000
Answer
Answer (as printed): B
Explanation
Let the length of each edge of small cube be $a_{1}$ and that of large cube be $a_{2}$. Then, $6 a_{1}{ }^{2}=96$ and $6 a_{2}{ }^{2}=384 \Rightarrow a_{1}{ }^{2}=16$ and $a_{2}{ }^{2}=64$ $\Rightarrow a_{1}=4$ and $a_{2}=8$. $$\begin{aligned} \therefore \text { Number of cubes formed } & =\frac{\text { Volume of larger cube }}{\text { Volume of smaller cube }} \\ & =\left(\frac{8 \times 8 \times 8}{4 \times 4 \times 4}\right)=8 \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.