A solid metallic cube having surface area of 54 cm² is melted to form smaller cubes of surface area cubes. $$\frac{8}{12}$$​ cm² each. Find the number of smaller.

Correct option is A

Given:
Surface area of cube = $$54 cm^2$$​​
Surface area of smaller cubes = $$\frac{8}{12}cm^2=\frac{2}{3}cm^2$$​​
Formula Used:
Surface area of cube = $$6a^2,$$​where a = side
Volume of cube = $$a^3$$​​
Total number of smaller cubes = $$\frac{ Volume \ of \ larger \ cube}{Volume \ of \ smaller \ cube}$$​​
Solution:
As per the question for larger cube,
​$$6a^2=54 \\\ \\a^2=\frac{54}{6}=9 \\\ \\a=√9=3$$​​
For the smaller cube,
​$$6a^2=\frac{2}{3}\\\ \\a^2=\frac{2}{18 } \\\ \\a=√(\frac{2}{18})=√(\frac{1}{9})=\frac{1}{3}$$​​
Total number of smaller cubes formed = $$\frac{3^3}{(\frac{1}{3})^3 }=\frac{27}{\frac{1}{27}}=27×27=729$$​​