Source: Extra Practice
The density of a solid cube is determined by measuring its mass and the length of its side. If the maximum error in the measurement of mass is and the maximum error in the measurement of length is , what is the maximum percentage error in the calculated density?
Options
Option A
5%
Option B
7%
Option C is correct
9%
Option D
11%
Explanation
Density is defined as . For a cube of side , the volume . Thus, . The relative error in density is given by . Converting this to percentage error: Percentage error in . Substituting the values: . Option 5% is incorrect because it simply adds the errors without accounting for the cubic relationship of length. Option 7% is incorrect calculation, and 11% is irrelevant.