When a ball of copper is heated, its diameter is observed to increase by 0.01%. We can say that it's volume increases by approximately

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The problem says a copper ball’s diameter increases by 0.01% when heated, and asks for the approximate relative change in volume due to this diameter change.
Option 1: 0.01% — This would be the relative change in diameter, not in volume. Since volume scales with the cube of the linear dimension, the volume change is larger than the diameter change.
Option 2: 0.03% — This comes from the fact that for small changes, ΔV/V ≈ 3 (ΔD/D) for a sphere, because V ∝ D^3. Here ΔD/D = 0.01% = 0.0001, so ΔV/V ≈ 3 × 0.0001 = 0.0003 = 0.03%. This aligns with the cubic dependence of volume on diameter.
Option 3: 0.000001% — This is far too small by several orders of magnitude. It would correspond to a much smaller exponent or an error in applying the proportionality, which is not the case for a simple geometric scaling.
Option 4: 0.02% — This is close but does not match the cubic relationship. It would arise if volume depended on D^2 (which it does not for a sphere), or if a miscalculation of the factor 3 occurred.
In summary, since volume scales with the cube of diameter, a 0.01% increase in diameter yields approximately a 0.03% increase in volume, via the relation ΔV/V ≈ 3 ΔD/D for small changes.

PHYS_V 157 201 2024W2 Reading Quiz Week 2

When a ball of copper is heated, its diameter is observed to increase by 0.01%. We can say that it's volume increases by approximately

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