Question

How will the volume of a cube change if its edge becomes twice as long; 3 times as long; 10 times as long; n times as long?

Answer 1

Let, initial side is a.

When side is n times long, new side na.

Initial volume, $V_i=a^3$

Final volume, $V_f=(na)^3=n^3a^3$

Change in volume, $V_f-V_i=\Delta V =a^3(n^3-1)$

For, n = 2 :

$\Delta V = 7a^3$

n = 3 :

$\Delta V = 26a^3$

n = 10 :

$\Delta V = 999a^3$

Hence, this is the required solution.