Question

Two similar cones have a scale factor of 8/27. What is the ratio of their volumes.

Answer 1

We have two cones.

They have a scale factor of 8:27.

This ratio relates elements in one dimension: radius, height, slant height.

This can be expressed for the height for example as:

`(h_2)/(h_1)=(8)/(27)`

If this is the ratio between the linear elements, then the ratio for the volume will be the cube of the linear ratio.

Then, we can find the ratio for the volumes as:

`(V_2)/(V_1)=((8)/(27))^3=(512)/(19683)`

Answer: if the scale factor of the cones is 8/27, the ratio of their volumes is 512/19683.