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Volume Scale Factor
Two similar solids have corresponding side lengths in the ratio 2:3. If the volume of the smaller solid is 40, what is the volume of the larger solid?
Need a hint?
Volume scales by the cube of the side-length scale factor.
Correct answer
D. 135
Solution
The side-length ratio is:
2:3
The volume ratio is:
23:33 = 8:27
The smaller volume corresponds to 8 parts:
8 parts = 40
1 part = 5
The larger volume is:
27 × 5 = 135
Detailed solution
For similar solids, the side ratio is not the volume ratio. Since volume is three-dimensional, the scale factor is cubed. That changes 2:3 into 8:27.
Common mistake
A common mistake is multiplying 40 by 32 and getting 60. That uses the length scale factor, not the volume scale factor.
Trap logic
The trap is using the side ratio directly on volume.
What this reveals
If this was missed, the weak point is dimensional scaling.
StudyGlitch notes
GAT similarity questions often test whether the quantity is length, area, or volume.
Length scale factor: first power. Area: square. Volume: cube.
Convert the side ratio 2:3 into volume ratio 8:27.
This week’s question is more than a score.
A wrong answer usually points to a pattern: slow recognition, a trap choice, weak setup, or pressure under time. Use this challenge as a signal, then connect it to your diagnostic, practice history, and weekly StudyGlitch progress.