Question

How many small cubes, each of $96c{m}^2$ surface area can be formed from the material obtained by melting a larger cube of $384c{m}^2$ surface area ?

• A. $80$
• B. $5$
• C. $800$
• D. $8$

Answer 1

Answer: (D)

$8$

Let the side of a bigger cube be $acm$ and that of smaller cube be $bcm$.

Area of bigger cube$=6a^2=384c{m}^2$ ...Given
$\therefore$$a=8cm$

Area of smaller cube$=6b^2=96c{m}^2$ ...Given
$\therefore$$b=4cm$

Number of cubes$=\frac{\text{Volume of bigger cube}}{\text{Volume of smaller cube}}$

$\therefore$ Number of cubes$=\frac{8\times 8\times 8}{4\times 4\times 4}=8$