Question

If two similar cones have volumes of 320cm^3 and 1,080cm^3, find the scale factor.

Answer 1

The ratio of the volumes is equal to the scale factor cubed.

$\frac{V_1}{V_2}=k^3 \\ \\ \frac{320 \ cm^3}{1080 \ cm^3}=k^3 \\ \frac{8}{27}=k^3 \\ k=\sqrt[3]{\frac{8}{27}} \\ \boxed{k=\frac{2}{3}} \Leftarrow \hbox{answer B}$