Gold is about 2.5 times as dense as iron, and iron is about 2.5 times as dense as aluminium. Roughly how many times denser than aluminium is gold?
AAbout 5 times as dense
BAbout 6 times as dense
CAbout 25 times as dense
DAbout 2.5 times as dense
Answer & Solution
Correct answer: B. About 6 times as dense
1. Density ratios chain by multiplication, not by addition.
2. Gold compared with iron gives a factor of 2.5, and iron compared with aluminium gives another factor of 2.5.
3. Gold compared with aluminium is therefore 2.5 multiplied by 2.5, which is 6.25, so about 6 times.
4. Adding the two factors would give 5, which is the trap set for anyone who sums ratios instead of multiplying them.
5. A factor of 25 would follow only if each step were a factor of 5.
_Source: OpenStax College Physics (CC BY 4.0), Ch 11 "Fluid Statics", section 11.2 Density_
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