Let, initial side is a.
When side is n times long, new side na.
Initial volume, [tex]V_i=a^3[/tex]
Final volume, [tex]V_f=(na)^3=n^3a^3[/tex]
Change in volume, [tex]V_f-V_i=\Delta V =a^3(n^3-1)[/tex]
For, n = 2 :
[tex]\Delta V = 7a^3[/tex]
n = 3 :
[tex]\Delta V = 26a^3[/tex]
n = 10 :
[tex]\Delta V = 999a^3[/tex]
Hence, this is the required solution.
