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The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are 4% and 3% respectively, the maximum error in the measurement of density will be:

1. 7%
2. 9%
3. 12%
4. 13%

Correct answer: 12%

Solution

The density of a cube is given by \( \rho = \frac{m}{l^3} \). The percentage error in density is \( \Delta \rho / \rho = \Delta m / m + 3(\Delta l / l) \). Substituting the given errors, \( 4\% + 3 \times 3\% = 12\% \).

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