Question

A solid metallic cube of edge $4$ cm is melted and recast into solid cubes of edge $1$ cm . If $x$ is the surface area of the melted cube and $y$ is the total surface area of the cubes recast, then what is $x:y$ ?

• A. $2:1$
• B. $1:2$
• C. $1:4$
• D. $4:1$

Answer 1

The correct option is C $1:4$

Volume of solid cube$={\left(4\right)}^3=64c{m}^3$

Volume of recast cube$={\left(1\right)}^4=1c{m}^3$

Number of cubes recast$=\frac{64}{1}=64$

TSA of solid cube$=6\times {\left(4\right)}^2=96$

TSA of recast cubes$=64\times 6\times 1^2=384$

$\therefore$Required ratio $=96:384=1:4$