Question

Two cubes have edges with a scale factor of 2 : 3. What is the ratio of their volumes?
1. 2 : 3
2. 4 : 9
3. 4 : 6
4. 8 : 27

Answer 1

Choice 4. 8:27
The volume of a cube: \[side^{3}\]
So let's say the sides of the cubes are 2 and 3, since that way the scale factor would still be 2:3 and the numbers are pretty easy to work with.
Calculate the volumes of the cubes:
\[2^{3}=8 units^3]\]
\[3^{3}= 27 units^3\]
8: 27, or 8/27 cannot be simplified. So the ratio of their volumes is 8:27.
(First time using the nice equation feature)