Question

The two right triangular prisms are similar solids.



The scale factor of the larger prism to the smaller prism is . How do the volumes compare?

The volume changes by .
The volume changes by , or .
The volume changes by , or .

Answer 1

I don’t see the scale factor number in your question — can you tell me the value (or attach the diagram)?

General method:
- If the linear scale factor from the smaller prism to the larger prism is k, then the volumes scale by k^3.
- So V(larger) = k^3 · V(smaller).
- As a percent change: percent increase = (k^3 − 1)·100% (if k>1). If k<1 it’s a percent decrease: (1 − k^3)·100%.

Examples:
- If k = 2, volumes compare 8:1 (volume changes by factor 8, i.e. an increase of 700%).
- If k = 3/2, volumes compare 27:8 (factor 27/8 ≈ 3.375, i.e. an increase of 237.5%).
- If k = 1/3, volumes compare 1:27 (factor 1/27 ≈ 0.037, i.e. a decrease of 96.3%).

Give the actual scale factor and I’ll fill in the blanks exactly.