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 numeric scale factor in your message. In general:

- If the linear scale factor (larger : smaller) is k, then the volume scale factor is k^3.
- So the larger prism’s volume = k^3 × (smaller prism’s volume).
- Equivalently, the volume “changes by” a factor of k^3, or by (k^3 − 1)·100% (increase if k>1, decrease if 0<k<1).

Give me the value of the scale factor (k) and I’ll fill in the specific numbers.