To determine the maximum error in the measurement of density, we can use the concept of relative error. The relative error in a quantity is the ratio of the maximum error in the measurement of that quantity to its actual value.
Let's assume the actual mass of the cube is M, and the actual length of its side is L. The actual density (D_actual) of the cube is given by:
D_actual = M / (L^3)
The maximum error in the measurement of mass is 0.3% of the actual mass, which can be expressed as:
Max error in mass = 0.003 * M
Similarly, the maximum error in the measurement of length is 0.2% of the actual length, which can be expressed as:
Max error in length = 0.002 * L
Using these values, we can calculate the maximum error in the measurement of density (Max error in density).
Max error in density = (Max error in mass) / M + 3 * (Max error in length) / L
Substituting the expressions for the maximum errors in mass and length:
Max error in density = (0.003 * M) / M + 3 * (0.002 * L) / L
Max error in density = 0.003 + 3 * 0.002
Max error in density = 0.003 + 0.006
Max error in density = 0.009
Therefore, the maximum error in the measurement of density is 0.9% (option C).
