Question

What will happen to the volume of the cube, if its edge is (a) tripled (b) reduced to one-fourth ?

Answer 1

Volume of cube $\propto (edge{)}^3$

Case 1: If edge is tripled.

$\frac{V_{old}}{V_{new}}=\frac{(edg{e}_{old}{)}^3}{(3edg{e}_{old}{)}^3}$

$V_{new}=27V_{old}$

Volume will increase by $27$ times.

Case 2: If edge is reduced to one-fourth.

$\frac{V_{old}}{V_{new}}=\frac{{\left(edg{e}_{old}\right)}^3}{{\left(\frac{edg{e}_{old}}{4}\right)}^3}$

$V_{new}=\frac{1}{64}{V}_{old}$

Volume will be decreased by $\frac{1}{64}$ times.