Question

A cube has a volume of 512 mm^3. If all sides of the cube are divided by 4, what will the resulting volume be?

A) 8 mm^3
B) 27 mm^3
C) 7.2 mm^3
D) 12 mm^3

Answer 1

`\bf \textit{volume of a cube}\\\\ V=s^3\qquad \boxed{s=(s)/(4)}\implies V=\left( \cfrac{s}{4} \right)^3\implies V=\cfrac{s^3}{4^3}\implies V=s^3\cdot \cfrac{1}{4^3} \\\\\\ V=s^3\cdot \cfrac{1}{64}\impliedby (1)/(64)\textit{ of the original volume, if the original was 512} \\\\\\ 512\cdot \cfrac{1}{64}\implies \cfrac{512}{64}`